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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2020, Volume 26, Number 4, Pages 255–267
DOI: https://doi.org/10.21538/0134-4889-2020-26-4-255-267
(Mi timm1780)
 

This article is cited in 1 scientific paper (total in 1 paper)

Periodic wavelets on a multidimensional sphere and their application for function approximation

N. I. Chernykhab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
Full-text PDF (259 kB) Citations (1)
References:
Abstract: The author's scheme for constructing a multiresolution analysis on a sphere in $\mathbb{R}^3$ with respect to the spherical coordinates, which was published in 2019, is extended to spheres in $\mathbb{R}^n$ $(n\ge 3)$. In contrast to other papers, only periodic wavelets on the axis and their tensor products are used. Approximation properties are studied only for the wavelets based on the simplest scalar wavelets of Kotel'nikov–Meyer type with the compact support of their Fourier transforms. The implementation of the idea of a smooth continuation of functions from a sphere to $2\pi$-periodic functions in the polar coordinates analytically (without the complicated geometric interpretation made by the author earlier in $\mathbb{R}^3$) turned out to be very simple.
Keywords: wavelet, scaling function, approximation.
Funding agency Grant number
Ural Mathematical Center
Ural Federal University named after the First President of Russia B. N. Yeltsin 02.A03.21.0006
This study is a part of the research carried out at the Ural Mathematical Center and was supported by the Russian Academic Excellence Project (agreement no. 02.A03.21.0006 of August 27, 2013, between the Ministry of Education and Science of the Russian Federation and Ural Federal University).
Received: 28.09.2020
Revised: 04.11.2020
Accepted: 16.11.2020
Bibliographic databases:
Document Type: Article
UDC: 517.518.832
MSC: 42A10, 42B35, 65N60
Language: Russian
Citation: N. I. Chernykh, “Periodic wavelets on a multidimensional sphere and their application for function approximation”, Trudy Inst. Mat. i Mekh. UrO RAN, 26, no. 4, 2020, 255–267
Citation in format AMSBIB
\Bibitem{Che20}
\by N.~I.~Chernykh
\paper Periodic wavelets on a multidimensional sphere and their application for function approximation
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2020
\vol 26
\issue 4
\pages 255--267
\mathnet{http://mi.mathnet.ru/timm1780}
\crossref{https://doi.org/10.21538/0134-4889-2020-26-4-255-267}
\elib{https://elibrary.ru/item.asp?id=44314673}
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  • https://www.mathnet.ru/eng/timm/v26/i4/p255
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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