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Measure-free viewpoint on p-adic and adelic wavelets
Linnaeus University, Faculty of Technology, Department of Mathematics.ORCID iD: 0000-0002-9857-0938
St.-Petersburg State Architecture and Civil Engineering University.
University of Pretoria.
2013 (English)In: P-Adic Numbers, Ultrametric Analysis, and Applications, ISSN 2070-0466, E-ISSN 2070-0474, Vol. 5, no 3, p. 204-217Article in journal (Refereed) Published
Abstract [en]

Recently there were presented new examples of MRAs based on p-adic and adelicwavelets. This is a note of the methodological nature. Its aim is embed all known examples MRAsinto the measure-free scheme based on abstract Hilbert space formalism. On the one hand, suchan embedding unifies the known examples of MRAs. On the other hand, the presented measure freescheme can be used for construction of new examples ofMRAs, especially in the infinite dimensionalcase. The last section of this paper is devoted to another abstract MRAs scheme based on Rieszspaces.We start paper with a review on p-adic and adelic wavelets.

Place, publisher, year, edition, pages
Springer, 2013. Vol. 5, no 3, p. 204-217
Keywords [en]
p-adic and adelic multiresolution analysis, operational multiresolution analysis, positive wavelets
National Category
Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-33663DOI: 10.1134/S2070046613030035Scopus ID: 2-s2.0-84939897927OAI: oai:DiVA.org:lnu-33663DiVA, id: diva2:710717
Available from: 2014-04-08 Created: 2014-04-08 Last updated: 2017-12-05Bibliographically approved

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Khrennikov, Andrei

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