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An infinite family of p-adic non-Haar wavelet bases and pseudo-differential operators
Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering. (mathematics)ORCID iD: 0000-0002-9857-0938
2009 (English)In: P-Adic Numbers, Ultrametric Analysis, and Applications, ISSN 2070-0466, E-ISSN 2070-0474, Vol. 1, no 3, p. 204-216Article in journal (Refereed) Published
Abstract [en]

In this paper an infinite family of new compactly supported non-Haar p-adic wavelet bases in L 2 (Q n p )  is constructed. We also study the connections between wavelet analysis and spectral analysis of p-adic pseudo-differential operators. A criterion for a multidimensional p-adic wavelet to be an eigenfunction for a pseudo-differential operator is derived. We prove that these wavelets are eigenfunctions of the fractional operator. Since many p-adic models use pseudo-differential operators (fractional operator), these results can be intensively used in these models.

Place, publisher, year, edition, pages
Berlin: Springer , 2009. Vol. 1, no 3, p. 204-216
National Category
Mathematics
Research subject
Mathematics, Mathematics
Identifiers
URN: urn:nbn:se:vxu:diva-7126DOI: 10.1134/S2070046609030030OAI: oai:DiVA.org:vxu-7126DiVA, id: diva2:293988
Available from: 2010-02-15 Created: 2010-02-15 Last updated: 2017-12-12Bibliographically approved

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Publisher's full texthttp://www.springerlink.com/content/t94j212124732308/?p=47e488a74fc7483aa250c2174fcfe0f6&pi=2

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Khrennikov, Andrei

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