$p$-Adic multidimensional wavelets and their application to $p$-adic pseudo-differential operators

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dc.creatorKhrennikov, A. Yu.
dc.creatorShelkovich, V. M.
dc.date2006-12-15
dc.date.accessioned2026-07-07T07:35:58Z
dc.date.available2026-07-07T07:35:58Z
dc.descriptionIn this paper we study some problems related with the theory of multidimensional $p$-adic wavelets in connection with the theory of multidimensional $p$-adic pseudo-differential operators (in the $p$-adic Lizorkin space). We introduce a new class of $n$-dimensional $p$-adic compactly supported wavelets. In one-dimensional case this class includes the Kozyrev $p$-adic wavelets. These wavelets (and their Fourier transforms) form an orthonormal complete basis in ${\cL}^2(\bQ_p^n)$. 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 Taibleson fractional operator. Since many $p$-adic models use pseudo-differential operators (fractional operator), these results can be intensively used in applications. Moreover, $p$-adic wavelets are used to construct solutions of linear and {\it semi-linear} pseudo-differential equations.
dc.identifierhttps://arxiv.org/abs/math-ph/0612049
dc.identifierhttp://arxiv.org/abs/math-ph/0612049
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/120274
dc.subjectMathematical Physics
dc.subjectGeneral Mathematics
dc.subjectPrimary 11F85, 42C40, 47G30; Secondary 26A33, 46F10
dc.title$p$-Adic multidimensional wavelets and their application to $p$-adic pseudo-differential operators
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