Abstract:
In this article we construct a Haar system on compact zero-dimensional abelian group as shifts and powers of some characters system. We find conditions under which a Fourier–Haar series of continuous function converge uniformly. We find groups for which Haar functions generated from one function by the operation of shifts, powers and dilations.
\Bibitem{Luk09}
\by S.~F.~Lukomskii
\paper Haar series on compact zero-dimensional abelian group
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2009
\vol 9
\issue 1
\pages 14--19
\mathnet{http://mi.mathnet.ru/isu28}
\crossref{https://doi.org/10.18500/1816-9791-2009-9-1-14-19}
\elib{https://elibrary.ru/item.asp?id=11903496}
Linking options:
https://www.mathnet.ru/eng/isu28
https://www.mathnet.ru/eng/isu/v9/i1/p14
This publication is cited in the following 11 articles:
V. I. Shcherbakov, “Jordan Test for the Haar-Type Systems”, Russ Math., 68:11 (2024), 53
Bespalov M.S., “Wavelet P-Analogs of the Discrete Haar Transform”, Izv. Sarat. Univ. Math. Mech. Infor., 21:4 (2021), 520–531
V. I. Shcherbakov, “Majorants of the Dirichlet Kernels and the Dini Pointwise Tests for Generalized Haar Systems”, Math. Notes, 101:3 (2017), 542–565
V. I. Shcherbakov, “Divergence of the Fourier series by generalized Haar systems at points of continuity of a function”, Russian Math. (Iz. VUZ), 60:1 (2016), 42–59
A. A. Baryshev, D. S. Lukomskii, S. F. Lukomskii, “Sistemy szhatii i sdvigov v zadache szhatiya izobrazhenii”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 14:4(2) (2014), 505–510
I. Ya. Novikov, M. A. Skopina, “Why Are Haar Bases in Various Structures the Same?”, Math. Notes, 91:6 (2012), 895–898
N. E. Komissarova, “Funktsii Lebega po sisteme Khaara na nul-mernykh kompaktnykh gruppakh”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 12:3 (2012), 30–36
S. F. Lukomskii, “Haar System on the Product of Groups of p-Adic Integers”, Math. Notes, 90:4 (2011), 517–532
Lukomskii S.F., “Haar system on a product of zero-dimensional compact groups”, Cent. Eur. J. Math., 9:3 (2011), 627–639
S. F. Lukomskii, “Multiresolution analysis on zero-dimensional Abelian groups and wavelets bases”, Sb. Math., 201:5 (2010), 669–691
Citation in format AMSBIB
Contact us: