FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2000, VOLUME 6, NUMBER 1, PAGES 81-92

On unconditional and absolute convergence of wavelet type series

S. V. Golovan

Abstract

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In this paper we consider wavelet type systems, i. e. systems of type

{ymn(x) = 2m/2 y (2mx - n)},

where y Î L2(R) such that $ supp y \Subset R $. Let E be a set of real numbers. We prove the equivalence of absolute and unconditional convergence almost everywhere on E of the series

Sm ³ 0, n Î Z amn ymn(x).

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Last modified: April 11, 2000