Browsing by Author "Lekesiz, Esra Guldogan"

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Citation - Scopus: 1
Finite Bivariate Biorthogonal I-Konhauser Polynomials
(Elsevier, 2026) Lekesiz, Esra Guldogan; Cekim, Bayram; Ozarslan, Mehmet Ali
In the present study, a finite set of biorthogonal polynomials in two variables, produced from Konhauser polynomials, is introduced. Some properties like Laplace transform, integral and operational representation, fractional calculus operators of this family are investigated. Also, we compute Fourier transform for this new set and discover a new family of finite biorthogonal functions with the help of Parseval's identity. Further, in order to have semigroup property, we modify this finite set by adding two new parameters and construct fractional calculus operators. Thus, integral equation and integral operator are obtained for the modified version.
Finite Orthogonal M Matrix Polynomials
(MDPI, 2025) Lekesiz, Esra Guldogan
In this study, we aim to construct a finite set of orthogonal matrix polynomials for the first time, along with their finite orthogonality, matrix differential equation, Rodrigues' formula, several recurrence relations including three-term relation, forward and backward shift operators, generating functions, integral representation and their relation with Jacobi matrix polynomials. Thus, the concept of "finite", which is used to impose parametric constraints for orthogonal polynomials, is transferred to the theory of matrix polynomials for the first time in the literature. Moreover, this family reduces to the finite orthogonal M polynomials in the scalar case when the degree is 1, thereby providing a matrix generalization of finite orthogonal M polynomials in one variable.