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Non-Haar p-adic wavelets and their application to pseudo-differential operators and equations
Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.ORCID iD: 0000-0002-9857-0938
2010 (English)In: Applied and Computational Harmonic Analysis, ISSN 1063-5203, E-ISSN 1096-603X, Vol. 28, no 1, 1-23 p.Article in journal (Refereed) Published
Abstract [en]

In the present paper an infinite family of new compactly supported non-Haar p-adic wavelet bases in is constructed. These bases cannot be constructed in the framework of any of known theories. We use the wavelet bases in the following applications: in the theory of p-adic pseudo-differential operators and equations. The connections between wavelet analysis and spectral analysis of p-adic pseudo-differential operators is studied. We derive a criterion for a multidimensional p-adic wavelet function to be an eigenfunction for a pseudo-differential operator and prove that our wavelets are eigenfunctions of the fractional operator. p-Adic wavelets are used to construct solutions of linear (the first and second order in t) and semi-linear evolutionary pseudo-differential equations. Since many p-adic models use pseudo-differential operators (fractional operator), our results can be intensively used in these models.

Place, publisher, year, edition, pages
2010. Vol. 28, no 1, 1-23 p.
Keyword [en]
p-Adic compactly supported wavelet bases, p-Adic pseudo-differential operators, Fractional operators, p-Adic pseudo-differential equations, p-Adic Lizorkin spaces
National Category
Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-6958DOI: 10.1016/j.acha.2009.05.007OAI: oai:DiVA.org:lnu-6958DiVA: diva2:332273
Available from: 2010-08-03 Created: 2010-08-03 Last updated: 2016-05-03Bibliographically approved

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Khrennikov, Andrei
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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf