Non-Haar $p$-adic wavelets and their application to pseudo-differential operators and equations

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dc.creatorKhrennikov, A. Yu.
dc.creatorShelkovich, V. M.
dc.date2008-08-25
dc.date.accessioned2026-07-07T09:58:15Z
dc.date.available2026-07-07T09:58:15Z
dc.descriptionIn this paper a countable family of new compactly supported {\em non-Haar} $p$-adic wavelet bases in ${\cL}^2(\bQ_p^n)$ is constructed. We use the wavelet bases in the following applications: in the theory of $p$-adic pseudo-differential operators and equations. Namely, we 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. In addition, $p$-adic wavelets are used to construct solutions of linear and semi-linear pseudo-differential equations. Since many $p$-adic models use pseudo-differential operators (fractional operator), these results can be intensively used in these models.
dc.identifierhttps://arxiv.org/abs/0808.3338
dc.identifierhttp://arxiv.org/abs/0808.3338
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167651
dc.subjectMathematical Physics
dc.subjectGeneral Mathematics
dc.subject11F85, 42C40, 47G30 (Primary); 26A33, 46F10 (Secondary)
dc.titleNon-Haar $p$-adic wavelets and their application to pseudo-differential operators and equations
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