Abstract
As remarked in [6], there is an analogue for Jacobi expansions of a relation between the rates of divergence of Cesàro means of different orders for Laguerre expansions [6, (1.9)]. The purpose of this note is to prove this remark (see Corollary below) and to determine the rate of divergence in those cases where the norms increase like some power of n (see Thm.). Our interest in this mainly lies in the fact that such a relation, being (nearly) independent of the parameters of the space and of the expansion, may be a particular instance of a relation between Cesàro means of some more general class of orthogonal expansions, rather than in the proof which, except for one additional step, consists in known arguments.
This author was supported by a DFG grant (Ne 171/3) which is gratefully acknowledged.
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Görlich, E., Markett, C. (1978). On a Relation between the Norms of Cesaro Means of Jacobi Expansions. In: Butzer, P.L., Szökefalvi-Nagy, B. (eds) Linear Spaces and Approximation / Lineare Räume und Approximation. International Series of Numerical Mathematics / Intermationale Schriftenreihe zur Numberischen Mathematik / Sùrie Internationale D’analyse Numùruque, vol 40. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7180-8_24
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