Researchers

Rahaf Al-Dakkak

Published in

Al-Baath University Journal - Series of Basic Sciences, Volume 45, Issue 8, April 2023.

Abstract

In this paper, we generalize the expansions in Fourier series with respect to Chebyshev polynomials of the first kind in some function spaces including the spaces L_p.

To obtain the desired we need a linear subspace in L₂ having some simple properties, it is denoted by D and called the test space, then we construct its dual space, denote it by D" and then proof that its elements are Fourier series satisfying some conditions, which we use to develop the expansions  in the spaces L_p. Then we use the results to solve some problems in several function spaces.

Keywords: Fourier Series, Special Functions, Chebyshev Polynomials, Orthogonal Expansions, Differential Operators, Spectral Theory.

Link to full paper

https://albaath-univ.edu.sy/journal/index.php/Science/article/view/2362/2164