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p-Adic wavelets and their applications
Russian Acad Sci.
Linnaeus University, Faculty of Technology, Department of Mathematics.ORCID iD: 0000-0002-9857-0938
2014 (English)In: Proceedings of the Steklov Institute of Mathematics, ISSN 0081-5438, E-ISSN 1531-8605, Vol. 285, no 1, p. 157-196Article in journal (Refereed) Published
Abstract [en]

The theory of p-adic wavelets is presented. One-dimensional and multidimensional wavelet bases and their relation to the spectral theory of pseudodifferential operators are discussed. For the first time, bases of compactly supported eigenvectors for p-adic pseudodifferential operators were considered by V.S. Vladimirov. In contrast to real wavelets, p-adic wavelets are related to the group representation theory; namely, the frames of p-adic wavelets are the orbits of p-adic transformation groups (systems of coherent states). A p-adic multiresolution analysis is considered and is shown to be a particular case of the construction of a p-adic wavelet frame as an orbit of the action of the affine group.

Place, publisher, year, edition, pages
2014. Vol. 285, no 1, p. 157-196
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-36864DOI: 10.1134/S0081543814040129ISI: 000339949700012Scopus ID: 2-s2.0-84926323154OAI: oai:DiVA.org:lnu-36864DiVA, id: diva2:745548
Available from: 2014-09-10 Created: 2014-09-10 Last updated: 2017-12-05Bibliographically approved

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Khrennikov, Andrei

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