Almost everywhere strong summability of double Walsh-Fourier series

Gát, György and Ushangi, Goginava (2015) Almost everywhere strong summability of double Walsh-Fourier series. JOURNAL OF CONTEMPORARY MATHEMATICAL ANALYSIS-ARMENIAN ACADEMY OF SCIENCES, 50 (1). pp. 1-13. ISSN 1068-3623

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Abstract

Let P denote the set of positive integers, N:=P∪{0}. Denote Z2 the dis- crete cyclic group of order 2, that is Z2 = {0, 1}, where the group operation is the modulo 2 addition and every subset is open. The Haar measure on Z2 is given such that the measure of a singleton is 1/2. Let G be the complete direct product of the countable infinite copies of the compact groups Z2. The elements of G are of the form x = (x0, x1, ..., xk , ...) with xk ∈ {0, 1} (k ∈ N) . The group operation on G is the coordinate-wise addition, the measure (de- note by μ) and the topology are the product measure and topology. The compact Abelian group G is called the Walsh group.

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