Browsing by Author "Aktas, Rabia"

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Citation - WoS: 4
Citation - Scopus: 3
Fourier Transforms of Some Finite Bivariate Orthogonal Polynomials
(Mdpi, 2021) Guldogan Lekesiz, Esra; Aktas, Rabia; Masjed-Jamei, Mohammad
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.
Citation - WoS: 4
Citation - Scopus: 5
A New Family of Orthogonal Polynomials in Three Variables
(Springer, 2020) Aktas, Rabia; Area, Ivan; Guldogan, Esra
In this paper we introduce a six-parameter generalization of the four-parameter three-variable polynomials on the simplex and we investigate the properties of these polynomials. Sparse recurrence relations are derived by using ladder relations for shifted univariate Jacobi polynomials and bivariate polynomials on the triangle. Via these sparse recurrence relations, second order partial differential equations are presented. Some connection relations are obtained between these polynomials. Also, new results for the four-parameter three-variable polynomials on the simplex are given. Finally, some generating functions are derived.
Citation - WoS: 1
Citation - Scopus: 1
On a Symmetric Generalization of Bivariate Sturm-Liouville Problems
(Springer Singapore Pte Ltd, 2022) Tefo, Yves Guemo; Aktas, Rabia; Area, Ivan; Lekesiz, Esra Guldogan
A new class of partial differential equations having symmetric orthogonal solutions is presented. The general equation is presented and orthogonality is obtained using the Sturm-Liouville approach. Conditions on the polynomial coefficients to have admissible partial differential equations are given. The general case is analyzed in detail, providing orthogonality weight function, three-term recurrence relations for the monic orthogonal polynomial solutions, as well as explicit form of these monic orthogonal polynomial solutions, which are solutions of an admissible and potentially self-adjoint linear second-order partial differential equation of hypergeometric type.
Citation - WoS: 4
Citation - Scopus: 3
Some Limit Relationships Between Some Two-Variable Finite and Infinite Sequences of Orthogonal Polynomials
(Taylor & Francis Ltd, 2021) Guldogan Lekesiz, Esra; Aktas, Rabia
The aim of paper is to give some limit relationships between finite and infinite sequences of orthogonal polynomials in two variables and to obtain the well-known relations of some infinite sets of two-variable orthogonal polynomials by taking limit of the properties verified by finite classes of two-variable orthogonal polynomials. Furthermore, the fourth-order partial differential equations satisfied by the polynomials, which are the products of finite orthogonal polynomials, are presented and by taking limit of the derived fourth-order equations, partial differential equations for some infinite sequences of two-variable orthogonal polynomials are found.