FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

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

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