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.)