Summation Kernels for Orthogonal Polynomial Systems

The convergence of weighted Fourier expansions with respect to orthogonal polynomial systems fP n : n 2 N 0 g is studied in certain Banach spaces B L 1 (), where the support of the orthogonality measure is assumed to be innnite and compact. We focus on orthogonal polynomial systems which induce a hypergroup structure on N 0 and a convolution structure on supp. Especially the Dirichlet kernel, a Fej er-type kernel and the de la Vall ee-Poussin kernel are studied, where we stress the analogy to the trigonometric case.