FOURIER COEFFICIENTS OF CONTINUOUS FUNCTIONS WITH RESPECT TO LOCALIZED HAAR SYSTEM

FOURIER COEFFICIENTS OF CONTINUOUS FUNCTIONS WITH RESPECT TO LOCALIZED HAAR SYSTEM

We construct a nontrivial example of a continuous function f* on [0, 1]² which is orthogonal to tensor products of Haar functions supported on intervals of the same length. This example clarifies the possible behaviour of Fourier coefficients of continuous functions with respect to a localized Haar...

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Main Authors: E. S. Belkina, Yu. V. Malykhin
Format: Article
Language:English
Published: Petrozavodsk State University 2017-06-01
Series:Проблемы анализа
Subjects:
fractals
Haar system
Haar wavelets
Online Access:http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=3871&lang=en
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spelling doaj-f255abcd98c342f78da65db3fc484c722021-07-02T01:44:22ZengPetrozavodsk State UniversityПроблемы анализа2306-34242306-34322017-06-016(24)110.15393/j3.art.2017.3871FOURIER COEFFICIENTS OF CONTINUOUS FUNCTIONS WITH RESPECT TO LOCALIZED HAAR SYSTEME. S. Belkina0Yu. V. Malykhin1Petrozavodsk State UniversitySteklov Mathematical InstituteWe construct a nontrivial example of a continuous function f* on [0, 1]² which is orthogonal to tensor products of Haar functions supported on intervals of the same length. This example clarifies the possible behaviour of Fourier coefficients of continuous functions with respect to a localized Haar system. The function f* has fractal structure. We give lower bounds on its smoothness.http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=3871&lang=enfractalsHaar systemHaar wavelets
collection DOAJ
language English
format Article
sources DOAJ
author E. S. Belkina
Yu. V. Malykhin
spellingShingle E. S. Belkina
Yu. V. Malykhin
FOURIER COEFFICIENTS OF CONTINUOUS FUNCTIONS WITH RESPECT TO LOCALIZED HAAR SYSTEM
Проблемы анализа
fractals
Haar system
Haar wavelets
author_facet E. S. Belkina
Yu. V. Malykhin
author_sort E. S. Belkina
title FOURIER COEFFICIENTS OF CONTINUOUS FUNCTIONS WITH RESPECT TO LOCALIZED HAAR SYSTEM
title_short FOURIER COEFFICIENTS OF CONTINUOUS FUNCTIONS WITH RESPECT TO LOCALIZED HAAR SYSTEM
title_full FOURIER COEFFICIENTS OF CONTINUOUS FUNCTIONS WITH RESPECT TO LOCALIZED HAAR SYSTEM
title_fullStr FOURIER COEFFICIENTS OF CONTINUOUS FUNCTIONS WITH RESPECT TO LOCALIZED HAAR SYSTEM
title_full_unstemmed FOURIER COEFFICIENTS OF CONTINUOUS FUNCTIONS WITH RESPECT TO LOCALIZED HAAR SYSTEM
title_sort fourier coefficients of continuous functions with respect to localized haar system
publisher Petrozavodsk State University
series Проблемы анализа
issn 2306-3424
2306-3432
publishDate 2017-06-01
description We construct a nontrivial example of a continuous function f* on [0, 1]² which is orthogonal to tensor products of Haar functions supported on intervals of the same length. This example clarifies the possible behaviour of Fourier coefficients of continuous functions with respect to a localized Haar system. The function f* has fractal structure. We give lower bounds on its smoothness.
topic fractals
Haar system
Haar wavelets
url http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=3871&lang=en
work_keys_str_mv AT esbelkina fouriercoefficientsofcontinuousfunctionswithrespecttolocalizedhaarsystem
AT yuvmalykhin fouriercoefficientsofcontinuousfunctionswithrespecttolocalizedhaarsystem
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