S. F. Lukomskii

activity

20122023

most citedTrees in Wavelet analysis on Vilenkin groups

6 citations · 10 across the 5 of their papers we have counts for

collaborators

5 papers

math.NT2023

On approximation by tight wavelet frames on the field of $p$ -adic numbers

S. F. Lukomskii, A. M. Vodolazov

We discuss the problem on approximation by tight step wavelet frames on the field $Q_{p}$ of $p$ -adic numbers. Let $G_{n} = {x = \sum_{k = n}^{\infty} x_{k} p^{k}}$ , $X$ be a set of cha…

math.FA2017

Discrete Riesz MRA on local fields of positive characteristic

G. S. Berdnikov, S. F. Lukomskii

We propose a method to construct Riesz MRA on local fields of positive characteristic and corresponding scaling step functions that generate it.

math.FA2017

Riesz Bounds of Spline Affine Systems

S. A. Chumachenko, S. F. Lukomskii, P. A. Terekhin

We construct a family of spline affine Riesz bases, i.e. sequences of dilations and translations generated by the special spline functions $ψ_{m}$ , and we prove that their Riesz boun…

math.FA2013★ 6 cited

Trees in Wavelet analysis on Vilenkin groups

S. F. Lukomskii

We consider a class of $(1, M)$ -elementary step functions on the $p$ -adic Vilenkin group. We prove that $(1, M)$ -elementary step function generates a MRA on $p$ -adic Vilenkin group i…

math.FA2012★ 4 cited

Step refinable functions and orthogonal MRA on $p$ -adic Vilenkin groups

S. F. Lukomskii

We find the necessary and sufficient conditions for refinable step function under which this function generates an orthogonal MRA in the $L_{2} (G)$ -spaces on Vilenkin grou…

On approximation by tight wavelet frames on the field of p-adic numbers

Discrete Riesz MRA on local fields of positive characteristic

Riesz Bounds of Spline Affine Systems

Trees in Wavelet analysis on Vilenkin groups

Step refinable functions and orthogonal MRA on p-adic Vilenkin groups

On approximation by tight wavelet frames on the field of $p$ -adic numbers

Step refinable functions and orthogonal MRA on $p$ -adic Vilenkin groups