Related papers: A note on the strong convergence of two-dimensiona…
The general Poisson summation formula of Mellin analysis can be considered as a quadrature formula for the positive real axis with remainder. For Mellin bandlimited functions it becomes an exact quadrature formula. Our main aim is to study…
The relationship between nonnegative polynomials and sums of squares is one of the central questions in real algebraic geometry. A modern approach is to look at nonnegative polynomials and sums of squares on a real variety. We survey the…
The main purpose of present paper is to determine some lower bounds for the quotient of the normalized hyper-Bessel function and its partial sum, as well as for the quotient of the derivative of normalized hyper-Bessel function and its…
The talk discusses preliminary results of an updated analysis of the strange quark mass from the scalar current QCD sum rules [1]. In particular the role of the scalar form factor which is a main ingredient in the analysis is especially…
We prove orthogonality relations for some analogs of trigonometric functions on a $q$-quadratic grid and introduce the corresponding $q$-Fourier series. We also discuss several other properties of this basic trigonometric system and the…
We study de la Vall\'ee Poussin means of Walsh--Fourier series associated with a nondecreasing window sequence. We establish a sharp criterion for almost everywhere convergence for integrable functions. We further show that, when this…
In this paper, we study the class of one dimensional singular integrals that converge in the sense of Cauchy principal value. In addition, we present a simple method for approximating such integrals.
We study the shifted convolution sums associated to completely multiplicative functions taking values in $\{\pm 1\}$ and give combinatorical proofs of two recent results in the direction of Chowla's conjecture. We also determine the…
We prove a summation formula for a bilateral series whose terms are products of two basic hypergeometric functions. In special cases, series of this type arise as matrix elements of quantum group representations.
Gaussian Quadrature is a well known technique for numerical integration. Recently Gaussian quadrature with respect to discrete measures corresponding to finite sums have found some new interest. In this paper we apply these ideas to…
Opened up by early contributions due to, among others, H. Bohr, Hardy-Riesz, Bohnenblust-Hille, Neder and Landau the last 20 years show a substantial revival of systematic research on ordinary Dirichlet series $\sum a_n n^{-s}$, and more…
The first objective of the paper is to estimate logarithmic partial derivative for meromorphic functions in several complex variables. Our estimations for logarithmic partial derivatives extend the results of Gundersen \cite{GG2} to the…
By exploring the theory of Guillera-Rogers, we evaluate some infinite series whose summands are quadratic irrationals, in terms of $\pi$ and special values of Dirichlet $L$-functions $ L_d(2)\equiv L(2,(\frac…
Motivated by the inverse Littlewood-Offord problem for linear forms, we study the concentration of quadratic forms. We show that if this form concentrates on a small ball with high probability, then the coefficients can be approximated by a…
This paper deals with the Cauchy-Dirichlet problem for the fractional Cahn-Hilliard equation. The main results consist of global (in time) existence of weak solutions, characterization of parabolic smoothing effects (implying under proper…
We prove upper and lower bounds for certain sums of products of fractional parts by using majoring and minorizing functions from Fourier analysis. In special cases the upper bounds are sharp if there exist counterexamples to the Littlewood…
In this rather computational paper, we determine certain representation numbers of ideals in real quadratic number fields explicitly in order to obtain a representation of the associated Dirichlet series in terms of Dirichlet L-functions…
The classical quadratic Gauss sum can be thought of as an exponential sum attached to a quadratic form on a cyclic group. We introduce an equivariant version of Gauss sum for arbitrary finite quadratic forms, which is an exponential sum…
The purpose of this note is to present several aspects of concentration phenomena in high dimensional geometry. At the heart of the study is a geometric analysis point of view coming from the theory of high dimensional convex bodies. The…
For 1<p<infty, and weight w in A_p, and function f in L^p(w), we show that the r-variation of the Walsh-Fourier sums are finite, for r sufficiently large as function of w. (That r is a function of w is necessary.) This strengthens a result…