This article is cited in 6 papers

Haar System on the Product of Groups of $p$-Adic Integers

S. F. Lukomskii

Saratov State University named after N. G. Chernyshevsky

Abstract: We present an algorithm for constructing dilation operators on the product of groups of $p$-adic integers and construct a system of Haar functions which is obtained from a single function by using the operations of contraction, translation, and raising to a power. In the two-dimensional case, we describe all the Haar bases.

Keywords: system of Haar functions, the group of $p$-adic integers, wavelet basis, Haar basis, compact group, quotient group, Rademacher function, dilation operator, cyclic subgroup, coset.

UDC: 517.51

Received: 16.12.2009
Revised: 08.11.2010

DOI: 10.4213/mzm8631

 English version: Mathematical Notes, 2011, 90:4, 517–532

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