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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2020, Volume 26, Number 4, Pages 224–233
DOI: https://doi.org/10.21538/0134-4889-2020-26-4-224-233
(Mi timm1777)
 

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

Interpolating orthogonal bases of an MRA and wavelets

E. A. Pleshchevaab

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 (196 kB) Citations (1)
References:
Abstract: The main goal of this paper is to construct orthonormal bases of a multiresolution analysis (MRA) that are interpolating on the grid $k/2^j$. We consider an orthonormal MRA and the corresponding wavelets. Based on this MRA and using orthogonal masks of the scaling functions, we construct new masks of scaling functions that satisfy the interpolation condition. In I. Daubechies's book it is proved that bases of an MRA that are interpolating and orthogonal simultaneously cannot have a compact support. In 2008, Yu.N. Subbotin and N.I. Chernykh suggested a method for modifying the Meyer scaling function in such a way that the basis formed by it is simultaneously orthogonal and interpolating. In the present paper we propose a method for modifying a wider class of scaling functions in such a way that the new scaling functions remain orthogonal and at the same time become interpolating. We start the construction with a mask of a scaling function and find necessary and sufficient conditions for the shifts of the scaling function obtained with the use of the modified mask to form an interpolating orthogonal system.
Keywords: orthogonal wavelet, interpolating wavelet, scaling function, basis, multiresolution analysis, mask of scaling function.
Funding agency Grant number
Ural Mathematical Center
This study is a part of the research carried out at the Ural Mathematical Center.
Received: 26.08.2020
Revised: 02.11.2020
Accepted: 09.11.2020
Bibliographic databases:
Document Type: Article
UDC: 517.5
MSC: 42C40
Language: Russian
Citation: E. A. Pleshcheva, “Interpolating orthogonal bases of an MRA and wavelets”, Trudy Inst. Mat. i Mekh. UrO RAN, 26, no. 4, 2020, 224–233
Citation in format AMSBIB
\Bibitem{Ple20}
\by E.~A.~Pleshcheva
\paper Interpolating orthogonal bases of an MRA and wavelets
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2020
\vol 26
\issue 4
\pages 224--233
\mathnet{http://mi.mathnet.ru/timm1777}
\crossref{https://doi.org/10.21538/0134-4889-2020-26-4-224-233}
\elib{https://elibrary.ru/item.asp?id=44314670}
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  • https://www.mathnet.ru/eng/timm/v26/i4/p224
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Trudy Instituta Matematiki i Mekhaniki UrO RAN
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    Full-text PDF :27
    References:23
     
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