Related papers: Special functions associated with positive linear …

The aim of this paper is to study generating functions for the coefficients of the classical superoscillatory function associated with weak measurements. We also establish some new relations between the superoscillatory coefficients and…

We follow a stream of the history of positive matrices and positive functionals, as applied to algebraic sums of squares decompositions, with emphasis on the interaction between classical moment problems, function theory of one or several…

We present an elementary proof of a conjecture by I. Ra\c{s}a which is an inequality involving Bernstein basis polynomials and convex functions. It was affirmed in positive very recently by the use of stochastic convex orderings. Moreover,…

Cylindric skew Schur functions, which are a generalisation of skew Schur functions, arise naturally in the study of P-partitions. Also, recent work of A. Postnikov shows they have a strong connection with a problem of considerable current…

We study a class of weight functions on $[-1,1]$, which are special cases of the general weights studied by Bernstein and Szeg\"o, as well as their extentions to the interval $[-a,1]$ for a continuous parameter $a>0$. These weights are…

A new Goodman-Sharma modification of the Baskakov operator is presented for approximation of bounded and continuous on $[0,\,\infty)$ functions. In our study on the approximation error of the proposed operator we prove direct and strong…

In this paper, we construct a linear positive operators q-parametric Szasz-Mirakjan operators generated by the q-Dunkl generalization of the exponential function. We obtain Korovkin's type approximation theorem for these operators and…

We have derived some new results for the Mellin transform formulas, as well as for the Gauss hypergeometric function. Also, we have found the connection between the Legendre functions of the second kind. Some of the results obtained we used…

For a broad class of Frechet-Lie supergroups we prove that there exists a correspondence between positive definite smooth superfunctions and matrix coefficients of unitary representations. We also give a characterization of linear…

The theory of the functional sequences and series is presented; uniformly convergent, convergent in the sense of a mean square and weakly convergent sequences and series are considered. Sequential approach to constructing generalized…

We introduce a new type of Bernstein operators, which can be used to approximate the functions with inner singularities. The direct and inverse results of the weighted approximation of this new type of combinations are given.

Given a positive definite binary quadratic form f, let r(n) = |{(x,y): f(x,y)=n}| denote its representation function. In this paper we study linear correlations of these functions. For example, if r_1, ..., r_k are representation functions,…

The approximation properties of the Aldaz-Kounchev-Render (AKR) operators are discussed and classes of functions for which these operators approximate better than the classical Bernstein operators are described. The new results are then…

For a linear ODE with indeterminate coefficients, we explicitly exhibit a fundamental system of solutions, in terms of the coefficients. We show that the generalized Wronskians of the fundamental system are given by an action of the Schur…

One of the main purposes of this article is to give functional equations and differential equations between Bernstein basis functions and generating functions of B-spline curves. Using these equations, very useful formulas containing the…

In their work on differential operators in positive characteristic, Smith and Van den Bergh define and study the derived functors of differential operators; they arise naturally as obstructions to differential operators reducing to positive…

We present several types of ordinary generating functions involving central binomial coefficients, harmonic numbers, and odd harmonic numbers. Our results complement those of Boyadzhiev from 2012 and Chen from 2016. Based on these…

Using a combinatorial description of the Bernstein operator and its action on Schur functions, we describe the formal power series solutions to a family of partial differential equations known as the 2-Toda hierarchy. We also characterize…

We construct explicit differential operators on hermitian modular forms, extending methods developed for Siegel modular forms. These differential operators are closely related to the two-variable spherical pluriharmonic polynomials. We…

In this paper I present a brief survey of the active area of Special Functions associated with Root Systems. The article is intended for a general mathematical audience. It will not suppose prerequisites on either special functions or root…