Best approximation by Vilenkin-like systems.
Fourier coefficients and absolute convergence on compact totally disconnected groups.
On almost even arithmetical functions via orthonormal systems on Vilenkin groups
On (C,1) summability of integrable functions with respect to the Walsh-Kaczmarz system
Let G be the Walsh group. For we prove the a. e. convergence σf → f(n → ∞), where is the nth (C,1) mean of f with respect to the Walsh-Kaczmarz system. Define the maximal operator We prove that σ* is of type (p,p) for all 1 < p ≤ ∞ and of weak type (1,1). Moreover, , where H is the Hardy space on the Walsh group.
On (C,1) summability for Vilenkin-like systems
We give a common generalization of the Walsh system, Vilenkin system, the character system of the group of 2-adic (m-adic) integers, the product system of normalized coordinate functions for continuous irreducible unitary representations of the coordinate groups of noncommutative Vilenkin groups, the UDMD product systems (defined by F. Schipp) and some other systems. We prove that for integrable functions σₙf → f (n → ∞) a.e., where σₙf is the nth (C,1) mean of f. (For the character system of the...
Almost everywhere convergence of Marcinkiewicz means of Fourier series on the group of 2-adic integers
We prove the almost everywhere convergence of the Marcinkiewicz means of integrable functions σₙf → f for every f ∈ L¹(I²), where I is the group of 2-adic integers.
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