6
6.0

Jun 30, 2018
06/18

by
Amílcar Branquinho; Edmundo J. Huertas; Fernando R. Rafaeli

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This paper deals with monic orthogonal polynomial sequences (MOPS in short) generated by a Geronimus canonical spectral transformation of a positive Borel measure $\mu$, i.e., \begin{equation*} \frac{1}{(x-c)}d\mu (x)+N\delta (x-c), \end{equation*} for some free parameter $N \in \mathbb{R}_{+}$ and shift $c$. We analyze the behavior of the corresponding MOPS. In particular, we obtain such a behavior when the mass $N$ tends to infinity as well as we characterize the precise values of $N$ such...

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1402.6256

6
6.0

Jun 30, 2018
06/18

by
Artur Nicolau

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We study differentiability properties of functions defined in the euclidean space in terms of a conical square function which is analogue to the classical square function introduced by Stein and Zygmund in the sixties. Pointwise differentiability can be characterized, modulo sets of Lebesgue measure zero, in terms of the finiteness of the conical square function. At the complement of this set, a Law of the Iterated Logarithm describes the maximal growth of the divided differences in terms of a...

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1404.1746

4
4.0

Jun 30, 2018
06/18

by
Uriel Kaufmann; Ivan Medri

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We study existence and nonexistence of strictly positive solutions for the elliptic problems of the form $Lu=m\left( x\right) u^{p}$ in a bounded open interval, with zero boundary conditions, where $L$ is a strongly uniformly elliptic differential operator, $p\in\left( 0,1\right) $, and $m$ is a function that changes sign. We also characterize the set of values $p$ for which the problem admits a solution, and in addition an existence result for other nonlinearities is presented.

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1405.3687

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4.0

Jun 30, 2018
06/18

by
Haifeng Xu; Binxian Yuan; Zuyi Zhang; Jiuru Zhou

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We consider a special symmetric matrix and obtain a similar formula as the one obtained by Weyl's criterion. Some applications of the formula are given, where we give a new way to calculate the integral of $\ln\Gamma(x)$ on $[0,1]$, and we claim that one class of matrices are not Hadamard matrices.

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1405.3649

3
3.0

Jun 30, 2018
06/18

by
Fatma Hira; Nihat Altinisik

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In this paper, we investigate the sampling analysis associated with discontinuous Sturm-Liouville problem which has transmission conditions at two points of discontinuity also contains an eigenparameter in a boundary condition and two transmission conditions. We establish briefly spectral properties of the problem and then we prove the sampling theorem associated with the problem.

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1406.0594

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27

Jun 30, 2018
06/18

by
Jingguo Lai

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We investigate the relation between Carleson sequence and balayage, and use this to give an easy proof of the equivalence of the L1-norms of the maximal function and the square function in non-honogeneous martingale settings.

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1411.5407

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5.0

Jun 30, 2018
06/18

by
Yulia Bibilo

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We consider a linear meromorphic system in the Birkhoff standard form. The construction of the isomonodromic deformation of it proposed by Bolibruch is discussed. This construction has some special characteristics because of resonant irregular singularity at the infinity.

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1412.2896

4
4.0

Jun 30, 2018
06/18

by
Charles F. Dunkl; George Gasper

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A summation formula is derived for the sum of the first m+1 terms of the 3F2(a,b,c;(a+b+1)/2,2c;1) series when c = -m is a negative integer. This summation formula is used to derive a formula for the sum of a terminating double hypergeometric series that arose in another project by one of us (C.D.)

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1412.4022

5
5.0

Jun 30, 2018
06/18

by
Ricardo Almeida; Delfim F. M. Torres

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We consider Hadamard fractional derivatives and integrals of variable fractional order. A new type of fractional operator, which we call the Hadamard-Marchaud fractional derivative, is also considered. The objective is to represent these operators as series of terms involving integer-order derivatives only, and then approximate the fractional operators by a finite sum. An upper bound formula for the error is provided. We exemplify our method by applying the proposed numerical procedure to the...

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1412.5229

12
12

Jun 26, 2018
06/18

by
Pablo Rocha

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In this note we show that if f belongs to Hp(Rn)\capLs(Rn), where 0 < p

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1502.07542

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13

Jun 27, 2018
06/18

by
Hendrik De Bie; Frank Sommen; Michael Wutzig

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It is well-known that the reproducing kernel of the space of spherical harmonics of fixed homogeneity is given by a Gegenbauer polynomial. By going over to complex variables and restricting to suitable bihomogeneous subspaces, one obtains a reproducing kernel expressed as a Jacobi polynomial, which leads to Koornwinder's celebrated result on the addition formula. In the present paper, the space of Hermitian monogenics, which is the space of polynomial bihomogeneous null-solutions of a set of...

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1503.03969

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10.0

Jun 27, 2018
06/18

by
Marek Galewski

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We consider a functional being a difference of two differentiable convex functionals on a closed ball. Existence and multiplicity of critical points is investigated. Some applications are given.

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1503.06874

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32

Jun 27, 2018
06/18

by
Eric T. Sawyer; Chun-Yen Shen; Ignacio Uriarte-Tuero

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We extend our previous work in arXiv:1302.5093v10 to obtain a T1 theorem with an energy side condition that allows for common point masses.

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1505.07816

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19

Jun 27, 2018
06/18

by
Subuhi Khan; Mumtaz Riyasat

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In this article, the 2-iterated Sheffer polynomials are introduced by means of generating function and operational representation. Using the theory of Riordan arrays and relations between the Sheffer sequences and Riordan arrays, a determinantal definition for these polynomials is established. The quasi-monomial and other properties of these polynomials are derived. The generating function, determinantal definition, quasi-monomial and other properties for some new members belonging to this...

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1506.00087

3
3.0

Jun 29, 2018
06/18

by
Sihun Jo; Minsuk Yang

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We investigate the second moment of a random sampling $\zeta(1/2+iX_t)$ of the Riemann zeta function on the critical line. Our main result states that if $X_t$ is an increasing random sampling with gamma distribution, then for all sufficiently large $t$, \[\mathbb{E} |\zeta(1/2+iX_t)|^2 = \log t + O(\sqrt{\log t}\log\log t).\]

Topics: Classical Analysis and ODEs, Mathematics

Source: http://arxiv.org/abs/1606.01179

5
5.0

Jun 29, 2018
06/18

by
O. Costin; R. D. Costin

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We construct a new type of convergent asymptotic representations, dyadic factorial expansions. Their convergence is geometric and the region of convergence can include Stokes rays, and often extends down to 0^+. For special functions such as Bessel, Airy, Ei, Erfc, Gamma and others, this region is C without an arbitrarily chosen ray effectively providing uniform convergent asymptotic expansions for special functions. We prove that relatively general functions, Ecalle resurgent ones possess...

Topics: Classical Analysis and ODEs, Mathematics

Source: http://arxiv.org/abs/1608.01010

3
3.0

Jun 29, 2018
06/18

by
Filip Pietrusiak

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We consider the following BVP $\ddot{x}\left( t\right) =f\left( t,\dot{x}\left( t\right) ,x\left( t\right) \right) -h\left( t\right) $, $% x\left( 0\right) =x\left( 1\right) =0$, where $f$ is continuous and satisfies some other conditions, $h\in H_{0}^{1}\left( 0,1\right) $ together with its discretization $$-\Delta^{2}x(k-1)+\frac{1}{n^{2}}f\left(\frac{k}{n}, n\Delta x\left(k-1\right), x\left(k\right)\right)=\frac{1}{n^{2}}h\left(\frac{k}{n}\right), k\in \left\{1, 2, \ldots,n \right\}.$$ Using...

Topics: Classical Analysis and ODEs, Mathematics

Source: http://arxiv.org/abs/1606.07120

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8.0

Jun 29, 2018
06/18

by
Dragana Jankov Maširević; Tibor K. Pogány

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Motivated by certain current results by Parmar and Pog\'any [9] in which the authors introduced the so-called $p$-extended Mathieu series the main aim of this paper is to present a connection between such series and a various types of Schl\"omilch series.

Topics: Classical Analysis and ODEs, Mathematics

Source: http://arxiv.org/abs/1606.08937

5
5.0

Jun 29, 2018
06/18

by
Guoen Hu

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Let $T$ be a singular integral operator with non-smooth kernel which were introduced by Duong and McIntosh. In this paper, we prove that this operator and its corresponding grand maximal operator satisfies certain weak type endpoint vector-valued estimate of $L\log L$ type. As an application we established a refined weighted vector-valued bound for this operator.

Topics: Classical Analysis and ODEs, Mathematics

Source: http://arxiv.org/abs/1607.05586

6
6.0

Jun 29, 2018
06/18

by
Tom H. Koornwinder

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We observe that the linearization coefficients for Gegenbauer polynomials are the orthogonality weights for Racah polynomials with special parameters. Then it turns out that the linearization sum with such a Racah polynomial as extra factor inserted, can also be evaluated. The corresponding Fourier-Racah expansion is an addition type formula which is dual to the well-known addition formula for Gegenbauer polynomials. The limit to the case of Hermite polynomials of this dual addition formula is...

Topics: Classical Analysis and ODEs, Mathematics

Source: http://arxiv.org/abs/1607.06053

4
4.0

Jun 29, 2018
06/18

by
C. Perez; I. Rivera-Rios; L. Roncal

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Quantitative $A_1-A_\infty$ estimates for rough homogeneous singular integrals $T_{\Omega}$ and commutators of $BMO$ symbols and $T_{\Omega}$ are obtained. In particular the following estimates are proved: % \[ \|T_\Omega \|_{L^p(w)}\le c_{n,p}\|\Omega\|_{L^\infty} [w]_{A_1}^{\frac{1}{p}}\,[w]_{A_{\infty}}^{1+\frac{1}{p'}}\|f\|_{L^p(w)} \] % and % \[ \| [b,T_{\Omega}]f\|_{L^{p}(w)}\leq c_{n,p}\|b\|_{BMO}\|\Omega\|_{L^{\infty}}...

Topics: Classical Analysis and ODEs, Mathematics

Source: http://arxiv.org/abs/1607.06432

6
6.0

Jun 29, 2018
06/18

by
Imran Abbas Baloch; Silvestru Sever Dragomir

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In this paper, we give the refinement of an extension of Jensen's inequality to affine combinations. Furthermore, we present the functional form of Jensen's inequality for continuous 3-convex functions of one variable at a point.

Topics: Classical Analysis and ODEs, Mathematics

Source: http://arxiv.org/abs/1601.06123

4
4.0

Jun 29, 2018
06/18

by
Luc Vinet; Alexei Zhedanov

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We introduce the notion of "hypergeometric" polynomials with respect to Newtonian bases. These polynomials are eigenfunctions ($L P_n(x) = \lambda_n P_n(x)$) of some abstract operator $L$ which is 2-diagonal in the Newtonian basis $\varphi_n(x)$: $L \varphi_n(x) = \lambda_n \varphi_n(x) + \tau_n(x) \varphi_{n-1}(x)$ with some coefficients $\lambda_n$, $\tau_n$. We find the necessary and sufficient conditions for the polynomials $P_n(x)$ to be orthogonal. For the special cases where...

Topics: Classical Analysis and ODEs, Mathematics

Source: http://arxiv.org/abs/1602.02724

4
4.0

Jun 29, 2018
06/18

by
N. D. Cong; T. S. Doan; H. T. Tuan

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We give a necessary and sufficient condition for a system of linear inhomogeneous fractional differential equations to have at least one bounded solution. We also obtain an explicit description for the set of all bounded (or decay) solutions for these systems.

Topics: Classical Analysis and ODEs, Mathematics

Source: http://arxiv.org/abs/1602.04695

4
4.0

Jun 30, 2018
06/18

by
Tiziana Cardinali; Radu Precup; Paola Rubbioni

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We investigate the effect of nonlocal conditions expressed by linear continuous mappings over the hypotheses which guarantee the existence of global mild solutions for functional-differential equations in a Banach space. A progressive transition from the Volterra integral operator associated to the Cauchy problem, to Fredholm type operators appears when the support of the nonlocal condition increases from zero to the entire interval of the problem. The results are extended to systems of...

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1406.6825

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7.0

Jun 30, 2018
06/18

by
Martin Himmel

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First we recall the notion of conxity and log-convexity for real-valued. Then we generalize the trick used by Artin in his famous paper on the Gamma function to find log-convex solutions to the functional equations f(x+1)=g(x)f(x). This gives rise to understand a function by its representer.

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1408.6715

3
3.0

Jun 30, 2018
06/18

by
Marcos Marvá

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In this work we provide a method for building up a strictly positive supersolution for the steady state of a degenerated logistic equation type, i.e., when the weight function vanishes on the boundary of the domain. This degenerated system is related in obtaining the so-called large solutions. Previously, this problem was handled as the limit case of non degenerated approaching problems. Our method can be adapted straightforwardly to degenerated boundary value problems.

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1409.6890

4
4.0

Jun 29, 2018
06/18

by
Dimitris Askitis

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In this paper, we shall study the asymptotic behaviour of the $p$-inverse of the Beta distribution, i.e. the quantity $q$ defined implicitly by $\int_0^q t^{a - 1} (1 - t)^{b - 1} \text{d} t = p B (a, b)$, as a function of the first parameter $a$. In particular, we study the monotonicity and limits of $q (a)$, as well as of $\varphi (a) = - a \log q (a)$ and we derive asymptotic expansions of $\varphi$ and $q$ at $0$ and $\infty$. Moreover, we prove some general results on $-inverses, with some...

Topics: Classical Analysis and ODEs, Mathematics

Source: http://arxiv.org/abs/1611.03573

5
5.0

Jun 29, 2018
06/18

by
Jagan Mohan Jonnalagadda

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In this article, we propose a novel matrix technique to obtain numerical solutions of initial value problems involving linear fractional nabla difference equations and provide few examples to illustrate the applicability of proposed method. In particular, we solve nabla analogue of fractional relaxation - oscillation equation numerically using this method.

Topics: Classical Analysis and ODEs, Mathematics

Source: http://arxiv.org/abs/1612.03766

5
5.0

Jun 30, 2018
06/18

by
Zhulin He; Yuyuan Ouyang

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We prove an inequality for Jacobi polynomials that \begin{align} \Delta_n(x):=P_n^{(\alpha_n,\beta_n)}(x)P_n^{(\alpha_{n+1},\beta_{n+1})}(x)- P_{n-1}^{(\alpha_n,\beta_n)}(x)P_{n+1}^{(\alpha_{n+1},\beta_{n+1})}(x)\le 0,\ \forall x\ge 1, \end{align} where $\alpha_n=an$ and $\beta_n=bn$ for some $a,b\ge 0$. The above inequality has a similar taste as the Tu\'ran type inequalities, but with $\alpha_n$ and $\beta_n$ that depends linearly on $n$.

Topics: Classical Analysis and ODEs, Mathematics

Source: http://arxiv.org/abs/1704.06381

5
5.0

Jun 30, 2018
06/18

by
F. P. da Costa; J. T. Pinto; R. Sasportes

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We study the behaviour as $t\to\infty$ of solutions $(c_j(t))$ to the Redner--Ben-Avraham--Kahng coagulation system with positive and compactly supported initial data, rigorously proving and slightly extending results originally established in [4] by means of formal arguments.

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1401.3715

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14

Jun 28, 2018
06/18

by
Zoltan M. Balogh; Orif O. Ibrogimov; Boris S. Mityagin

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The aim of this note is to characterize all pairs of sufficiently smooth functions for which the mean value in the Cauchy Mean Value Theorem is taken at a point which has a well-determined position in the interval. As an application of this result, a partial answer is given to a question posed by Sahoo and Riedel.

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1508.00329

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13

Jun 28, 2018
06/18

by
Annamaria Montanari; Daniele Morbidelli

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We show by explicit estimates that the SubRiemannian distance in a Carnot group of step two is locally semiconcave away from the diagonal if and only if the group does not contain abnormal minimizing curves. Moreover, we prove that local semiconcavity fails to hold in the step-3 Engel group, even in the weaker "horizontal" sense.

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1508.00997

13
13

Jun 28, 2018
06/18

by
Sigrid B. Heineken; Patricia M. Morillas

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A new notion of dual fusion frame has been recently introduced by the authors. In this article that notion is further motivated and it is shown that it is suitable to deal with questions posed in a finite-dimensional real or complex Hilbert space, reinforcing the idea that this concept of duality solves the question about an appropriate definition of dual fusion frames. It is shown that for overcomplete fusion frames there always exist duals different from the canonical one. Conditions that...

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1509.07724

4
4.0

Jun 28, 2018
06/18

by
Alan Horwitz

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We consider a problem similar to the well-known ladder box problem, but where the box is replaced by an ellipse. A ladder of a given length, $s$, with ends on the positive x and y axes, is known to touch an ellipse that lies in the first quadrant and is tangent to the positive x and y axes. We then want to find the height of the top of the ladder above the floor. We show that there is a value, $s = s_0$, such that there is only one possible position of the ladder, while if $s > s_0$, then...

Topics: Classical Analysis and ODEs, Mathematics

Source: http://arxiv.org/abs/1510.02051

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16

Jun 28, 2018
06/18

by
Irina Holmes; Robert Rahm; Scott Spencer

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In this paper we investigate weighted norm inequalities for the commutator of a fractional integral operator and multiplication by a function. In particular, we show that, for $\mu,\lambda\in A_{p,q}$ and $\alpha/n+1/q=1/p$, the norm $\| [b,I_\alpha]:L^p(\mu^p)\to L^q(\lambda^q) \|$ is equivalent to the norm of $b$ in the weighted BMO space $BMO(\nu)$, where $\nu=\mu\lambda^{-1}$. This work extends some of the results on this topic existing in the literature, and continues a line of...

Topics: Classical Analysis and ODEs, Mathematics

Source: http://arxiv.org/abs/1510.05331

4
4.0

Jun 28, 2018
06/18

by
Witold Jarczyk; Zsolt Páles

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In this paper, two parallel notions of convexity of sets are introduced in the abelian semigroup setting. The connection of these notions to algebraic and to set-theoretic operations is investigated. A formula for the computation of the convex hull is derived. Finally, a Stone-type separation theorem for disjoint convex sets is established.

Topics: Classical Analysis and ODEs, Mathematics

Source: http://arxiv.org/abs/1512.07275

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5.0

Jun 29, 2018
06/18

by
Abdullah Akkurt; M. Esra Yildirim; Hüseyin Yildirim

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In this paper, we consider a new class of convex functions which is called $\lambda$-preinvex functions. We prove several Hermite-Hadamard type inequalities for differentiable $\lambda$-preinvex functions via Fractional Integrals. Some special cases are also discussed.

Topics: Classical Analysis and ODEs, Mathematics

Source: http://arxiv.org/abs/1603.02070

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6.0

Jun 29, 2018
06/18

by
A. Kirtadze; G. Pantsulaia; N. Rusiashvili

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The concept of uniform distribution in $[0,1]$ is extended for a certain strictly separated maximal (in the sense of cardinality) family $(\lambda_t)_{t \in [0,1]}$ of invariant extensions of the linear Lebesgue measure $\lambda$ in $[0.1]$, and it is shown that the $\lambda_t^{\infty}$ measure of the set of all $\lambda_t$-uniformly distributed sequences is equal to $1$, where $\lambda_t^{\infty}$ denotes the infinite power of the measure $\lambda_t$. This is an analogue of Hlawka's (1956)...

Topics: Classical Analysis and ODEs, Mathematics

Source: http://arxiv.org/abs/1603.04472

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4.0

Jun 29, 2018
06/18

by
Manas R. Sahoo

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In this paper we show that certain sets are dense in $\mathbb{R}$. We give some applications. For example, we show an analytical proof that $q^{\frac{1}{n}}$, $q$ is a prime number and $e$; are irrational numbers. As another application we show: If $f$ is an locally integrable function on $\mathbb{R}-\{0\}$ satisfying $\int_x ^{px}f(t)dt$ and $\int_x ^{qx}f(t)dt$ are constant with $\frac{\ln p}{\ln q}$ is an irrational number; implies $f(t)=\frac{c}{t}\,\,\ a.e.$, where $c$ is constant; which...

Topics: Classical Analysis and ODEs, Mathematics

Source: http://arxiv.org/abs/1603.05331

6
6.0

Jun 29, 2018
06/18

by
Doowon Koh

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We study the extension estimates for paraboloids in d-dimensional vector spaces over finite fields F_q with q elements. We use the connection between L^2 based restriction estimates and L^p\to L^r extension estimates for paraboloids. As a consequence, we improve the L^2\to L^r extension results obtained by A. Lewko and M. Lewko in even dimensions d\ge 6 and odd dimensions d=4\ell+3 for \ell \in \mathbb N. Our results extend the consequences for 3-D paraboloids due to M. Lewko to higher...

Topics: Classical Analysis and ODEs, Mathematics

Source: http://arxiv.org/abs/1603.06512

4
4.0

Jun 29, 2018
06/18

by
Gökalp Alpan

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Let $K$ be a non-polar compact subset of $\mathbb{R}$ and $\mu_K$ denote the equilibrium measure of $K$. Furthermore, let $P_n\left(\cdot, \mu_K\right)$ be the $n$-th monic orthogonal polynomial for $\mu_K$. It is shown that $\|P_n\left(\cdot, \mu_K\right)\|_{L^2(\mu_K)}$, the Hilbert norm of $P_n\left(\cdot, \mu_K\right)$ in $L^2(\mu_K)$, is bounded below by $\mathrm{Cap}(K)^n$ for each $n\in\mathbb{N}$. A sufficient condition is given for...

Topics: Classical Analysis and ODEs, Mathematics

Source: http://arxiv.org/abs/1603.07705

4
4.0

Jun 29, 2018
06/18

by
Vincent X. Genest; Satoshi Tsujimoto; Luc Vinet; Alexei Zhedanov

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Persymmetric Jacobi matrices are invariant under reflection with respect to the anti-diagonal. The associated orthogonal polynomials have distinctive properties that are discussed. They are found in particular to be also orthogonal on the restrictions either to the odd or to the even points of the complete orthogonality lattice. This is exploited to design very efficient inverse problem algorithms for the reconstruction of persymmetric Jacobi matrices from spectral points. Isospectral...

Topics: Classical Analysis and ODEs, Mathematics

Source: http://arxiv.org/abs/1605.00708

5
5.0

Jun 29, 2018
06/18

by
Geno Nikolov; Alexei Shadrin

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Let $w_{\alpha}(t)=t^{\alpha}\,e^{-t}$, $\alpha>-1$, be the Laguerre weight function, and $|\cdot|_{w_\alpha}$ denote the associated $L_2$-norm, i.e., $$ | f|_{w_\alpha}:=\Big(\int_{0}^{\infty}w_{\alpha}(t)| f(t)|^2\,dt\Big)^{1/2}. $$ Denote by ${\cal P}_n$ the set of algebraic polynomials of degree not exceeding $n$. We study the best constant $c_n(\alpha)$ in the Markov inequality in this norm, $$ | p^{\prime}|_{w_\alpha}\leq c_n(\alpha)\,| p|_{w_\alpha}\,,\quad p\in {\cal P}_n\,, $$...

Topics: Classical Analysis and ODEs, Mathematics

Source: http://arxiv.org/abs/1605.02508

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4.0

Jun 30, 2018
06/18

by
Luís Daniel Abreu; João Pereira; José Luis Romero

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We investigate an inverse problem in time-frequency localization: the approximation of the symbol of a time-frequency localization operator from partial spectral information by the method of accumulated spectrograms (the sum of the spectrograms corresponding to large eigenvalues). We derive a sharp bound for the rate of convergence of the accumulated spectrogram, improving on recent results.

Topics: Classical Analysis and ODEs, Mathematics

Source: http://arxiv.org/abs/1704.02266

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Jun 27, 2018
06/18

by
Akane Nakamura

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Higher dimensional analogs of the Painlev\'e equations have been proposed from various aspects. In recent studies, 4-dimensional analogs of the Painlev\'e equations were classified into 40 types. The aim of the present paper is to geometrically characterize these 40 types of equations. For this purpose, we study the autonomous limit of these equations and degeneration of their spectral curves. We obtain two functionally independent conserved quantities $H_1$ and $H_2$ for each system. We...

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1505.00885

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Jun 27, 2018
06/18

by
Carlos Domingo-Salazar; Michael T. Lacey; Guillermo Rey

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For any Calder\'on-Zygmund operator $ T$, any weight $ w$, and $ \alpha >1$, the operator $ T$ is bounded as a map from $ L ^{1} (M _{ L \log\log L (\log\log\log L) ^{\alpha } } w )$ into weak-$L^1(w)$. The interest in questions of this type goes back to the beginnings of the weighted theory, with prior results, due to Coifman-Fefferman, P\'erez, and Hyt\"onen-P\'erez, on the $ L (\log L) ^{\epsilon }$ scale. Also, for square functions $ S f$, and weights $ w \in A_p$, the norm of $ S$...

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1505.01804

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Jun 27, 2018
06/18

by
Jacob S. Christiansen; Barry Simon; Maxim Zinchenko

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We consider Chebyshev polynomials, $T_n(z)$, for infinite, compact sets $\frak{e} \subset \mathbb{R}$ (that is, the monic polynomials minimizing the sup-norm, $\Vert T_n \Vert_{\frak{e}}$, on $\frak{e}$). We resolve a $45+$ year old conjecture of Widom that for finite gap subsets of $\mathbb{R}$, his conjectured asymptotics (which we call Szeg\H{o}-Widom asymptotics) holds. We also prove the first upper bounds of the form $\Vert T_n \Vert_{\frak{e}} \leq Q C({\frak{e}})^n$ (where $C(\frak{e})$...

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1505.02604

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6.0

Jun 27, 2018
06/18

by
Jean C. Guella; Valdir A. Menegatto

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For the real, continuous, isotropic and positive definite kernels on a product of spheres, one may consider not only its usual strict positive definiteness but also strict positive definiteness restrict to the points of the product that have distinct components. In this paper, we provide a characterization for strict positive definiteness in these two cases, settling all the cases but those in which one of the spheres is a circle.

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1505.03695

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Jun 28, 2018
06/18

by
Mohamed Jalel Atia; Faouzi Thabet

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In this paper, we discuss the representability almost everywhere (a.e.) in the plane of an irreducible algebraic function as the Cauchy transform of a signed measure supported on a finite number of compact semi-analytic curves and a finite number of isolated points. We discuss the existence of critical trajectories of a family of quadratic differentials.

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1506.06543