Results 141 to 150 of about 17,183,410 (158)

On the orthogonality of a system of shifts of the scaling function on Vilenkin groups

Mathematical Notes, 2015
This short paper is concerned with the problem of constructing an orthogonal scaling function and of avoiding the exhaustive search. The authors reduce the problem of constructing such a function to determining a graph that could be constructed from an arbitrary \(N\)-valid tree.
Lukomskii, S. F., Berdnikov, G. S., Kruss, Yu. S.   +2 more
openaire   +2 more sources

Integrals of weighted maximal kernels with respect to Vilenkin systems

Publicationes Mathematicae Debrecen, 2007
Summary: The integrals of maximal Dirichlet- and Fejér kernels are infinite, so we have to use some weight function to ``pull them back'' to the finite. In this paper we give necessary and sufficient conditions for weight functions to get finite integrals on arbitrary Vilenkin groups.
Mező, István, Simon, Péter
openaire   +2 more sources

Best approximation by Vilenkin-like systems

2001
The author introduces the notion of the modulus of continuity on Vilenkin spaces and the concept of the best approximation by Vilenkin-like polynomials. With this concept, among others, he proves a Jackson-type theorem. Furthermore, he presents a common generalization of the Walsh-Vilenkin system, the character system of the group of 2- and \(m\)-adic ...
openaire   +1 more source

(C, 1)-Summation of fourier series over rearranged Vilenkin system

Moscow University Mathematics Bulletin, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

Convergence of Marcinkiewicz Means of Integrable Functions with Respect to Two-Dimensional Vilenkin Systems

gmj, 2004
Abstract We prove that the maximal operator of the Marcinkiewicz mean of integrable two-variable functions is of weak type (1, 1) on bounded two-dimensional Vilenkin groups. Moreover, for any integrable function 𝑓 the Marcinkiewicz mean σ 𝑛𝑓 converges to 𝑓 almost everywhere.
openaire   +2 more sources

Convergence of Cesàro means of functions with respect to unbounded Vilenkin systems

2004
Summary: One of the most celebrated problems in dyadic harmonic analysis is the pointwise convergence of the Fejér (or (C,1)) means of functions on unbounded Vilenkin groups. The aim of this paper is to give a resume of the recent developments concerning this matter.
openaire   +1 more source

Relation between Dirichlet kernels with respect to Vilenkin-like systems

1994
Let \( m:= (m_k , k\in N) ( N:= \{ 0,1,\dots \} )\) be a sequence of integers not less than \(2\). Let \(Z_{m_k}\) be the \(m_k\)-th discrete cyclic group with Haar measure defined so that the measure of a singleton is \(1/m_k (k\in N).\) Let \(G_m := \prod_{k=0}^{\infty}Z_{m_k}\) with the product topology and measure. The system \((\psi _n : n\in N)\)
openaire   +2 more sources

On a norm convergence theorem with respect to the Vilenkin system in the Hardy spaces

1994
The author shows that his former result: \[ \lim_{n\to\infty}{1\over\log n}\sum_{k=1}^n|S_kf|_1/k=|f|_1 \] holds for functions in \(H(G_m)\) (the so-called ``atomic'' Hardy space) with respect to all \(G_m\) Vilenkin groups, and does not hold for unbounded Vilenkin groups and the ``maximal'' Hardy space.
openaire   +2 more sources

Approximation by Marcinkiewicz-Type Matrix Transform of Vilenkin–Fourier Series

Mediterranean Journal of Mathematics, 2022
István Blahota
exaly  

On the Nörlund logarithmic means with respect to Vilenkin system in the martingale Hardy space H 1

Acta Mathematica Hungarica, 2017
Giorgi Tephnadze, P Wall
exaly