EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 58(72), pp. 21--34 (1995)

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Summability of trigonometric series and Calderon reproducing formulas

W.O. Bray

Department of Mathematics, University of Maine Orono, Maine 04469, USA

Abstract: We show how to associate a Calderon reproducing formula with a number of summability methods, including Abel-Poisson, Gaussian, Riesz typical and Bochner-Riesz means. Such formula contains local/global information concerning the trigonometric series being summed whether it be a Fourier series or not. Consequently a number of classical results of Littlewood--Paley type are unified as well as related results concerning the function class Fourier character of trigonometric series. The paper also provides classical insight and heuristics concerning much contemporary work falling under the name of wavelet analysis.

Classification (MSC2000): 42A24, 42A16

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Electronic fulltext finalized on: 1 Nov 2001. This page was last modified: 16 Nov 2001.

© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
© 2001 ELibM for the EMIS Electronic Edition