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 \emph{wavelet type} systems, i. e.\ systems of type
$$
\{ \psi_{mn}(x) = 2^{m/2} \psi(2^mx-n) \},
$$
 where $\psi \in L^2 (\mathbb R)$ such that $\supp \psi \Subset \mathbb R$. Let $E$ be a set of real numbers. We prove the equivalence of absolute and unconditional convergence almost everywhere on $E$ of the series
$$
\sum_{\substack{m \geq 0\\ n \in \mathbb Z}} a_{mn} \psi_{mn}(x).
$$

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Last modified: April 11, 2000