ACTA issues

## On the convergence of weighted Fourier expansions with respect to orthogonal polynomials

R. Lasser, J. Obermaier

Acta Sci. Math. (Szeged) 61:1-4(1995), 345-355
5690/2009

 Abstract. The convergence of weighted Fourier expansions with respect to orthogonal polynomials is studied in the spaces $C(S)$ and $L^p(\pi )$, $1 \leq p < \infty$, where the support $S$ of the orthogonal measure $\pi$ is assumed to be compact. Necessary and sufficient conditions for convergence are given. The Dirichlet kernel is regarded especially in case of Jacobi polynomials. A Fejér-like kernel is introduced for a restricted class of orthogonal polynomials. Assuming the existence of a convolution structure on $C(S),$ the convergence of Fejér-like expansions is proved, particularly for Jacobi polynomials and generalized Chebyshev polynomials. AMS Subject Classification (1991): 42C15 Received May 25, 1994, and in revised form December 2, 1994. (Registered under 5690/2009.)