Analytic Wavelets in Multiply Connected Domains with Circular Boundaries

G. A. Dubosarskij<sup>ab

a</sup> Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
^b Institute of Mathematics and Computer Science, Ural Federal University, Ekaterinburg

Abstract: Wavelet bases in Hardy-type spaces of analytic functions in a domain with circular boundaries are constructed from a wavelet basis in the Hardy space of functions analytic in the disk. An estimate of the rate of convergence of the partial sums of the constructed wavelets is also obtained.

Keywords: analytic wavelet, basis in a Hardy-type space of analytic functions, wavelet expansion.

UDC: 517.538.2

Received: 05.04.2012
Revised: 08.04.2013

DOI: 10.4213/mzm9691

 English version: Mathematical Notes, 2014, 95:3, 359–373

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