ABSTRACT
The convergence of weighted Fourier expansions with respect to orthogonal polynomial systems {P n : n ∈ ℕ0} is studied in certain Banach spaces B ⊆ L 1(π), where the support of the orthogonality measure π is assumed to be infinite and compact. We focus on orthogonal polynomial systems which induce a hypergroup structure on ℕ0 and a convolution structure on supp π. Especially the Dirichlet kernel, a Fejér-type kernel and the de la Vallée-Poussin kernel are studied, where we stress the analogy to the trigonometric case.
