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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2016, Volume 22, Number 3, Pages 76–89
DOI: https://doi.org/10.21538/0134-4889-2016-22-3-76-89 (Mi timm1323) 		 
Biharmonic wavelets and their applications

G. A. Dubosarskii

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
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DOI: https://doi.org/10.21538/0134-4889-2016-22-3-76-89
Abstract: We propose a solution method for the basic boundary value problem for biharmonic functions. In this method, a special system of functions is orthogonalized and Fourier series in this system are considered. It is proved that the constructed series converge inside the domain. Biharmonic wavelets are constructed based on the orthogonalized system. It is established that series of wavelets converge uniformly in the domain with boundary.
Keywords: biharmonic function, boundary value problem, wavelets.
Funding agency Grant number
Russian Science Foundation 14-11-00702
Received: 16.03.2016
Bibliographic databases:
Document Type: Article
UDC: 517.544
MSC: 31B30
Language: Russian
Citation: G. A. Dubosarskii, “Biharmonic wavelets and their applications”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 3, 2016, 76–89
Citation in format AMSBIB
\Bibitem{Dub16}
\by G.~A.~Dubosarskii
\paper Biharmonic wavelets and their applications
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2016
\vol 22
\issue 3
\pages 76--89
\mathnet{http://mi.mathnet.ru/timm1323}
\crossref{https://doi.org/10.21538/0134-4889-2016-22-3-76-89}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3555712}
\elib{https://elibrary.ru/item.asp?id=26530879}
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