Abstract
In this paper, we first obtain the Fourier transforms of some finite bivariate orthogonal polynomials and then by using the Parseval identity, we introduce some new families of bivariate orthogonal functions.
Highlights
The families of orthogonal polynomials which are mapped onto each other can be introduced by using the well-known Fourier transform or other integral transforms [19]
We first consider Fourier transforms of some specific functions in terms of finite bivariate orthogonal polynomials listed above except for tenth, eleventh and twelft polynomial sequences and we introduce new families of bivariate orthogonal functions via Parseval identity
Fourier transforms of Jacobi, generalized Ultraspherical, generalized Hermite, Routh-Romanovski polynomials, finite classical orthogonal polynomials, etc. and relations with other polynomials have been studied by many authors
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. In [27] some new families of orthogonal functions in two variables were introduced by using Fourier transforms of specific functions derived from two-variable polynomials defined in [28,29] and using the Parseval identity their orthogonality relations have been obtained. This approach allows us to derive new families of bivariate orthogonal functions. The aim of this paper is to obtain new families of bivariate orthogonal functions by two-dimensional Fourier transforms of bivariate finite orthogonal polynomials given in [30] by means of Koorwinder’s method.
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