Non-Haar \(p\)-adic wavelets and pseudodifferential operators

DOI10.1134/S1064562408010110zbMath1213.42147OpenAlexW2082260572MaRDI QIDQ960653

Vladimir Shelkovich, Andrei Yu. Khrennikov

Publication date: 5 January 2009

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562408010110

zbMATH Keywords

eigenfunction\(p\)-adic pseudodifferential operators\(p\)-adic wavelets

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Pseudodifferential operators as generalizations of partial differential operators (35S05) Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) Pseudodifferential operators (47G30)

Related Items (8)

\(p\)-adic mathematical physics: the first 30 years ⋮ The Cauchy problems for evolutionary pseudo-differential equations over \(p\)-adic field and the wavelet theory ⋮ Transport through a network of capillaries from ultrametric diffusion equation with quadratic nonlinearity ⋮ \(p\)-adic wavelets and their applications ⋮ An infinite family of \(p\)-adic non-Haar wavelet bases and pseudo-differential operators ⋮ \(p\)-adic multiwavelet sets ⋮ Non-Haar \(p\)-adic wavelets and their application to pseudo-differential operators and equations ⋮ Unnamed Item

Cites Work

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• Localization in space for a free particle in ultrametric quantum mechanics
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• \(p\) -adic semilinear evolutionary pseudodifferential equations in Lizorkin spaces
• Wavelets on ultrametric spaces
• Harmonic analysis in the \(p\)-adic Lizorkin spaces: Fractional operators, pseudo-differential equations, \(p\)-adic wavelets, Tauberian theorems
• Harmonic analysis on \(n\)-dimensional vector spaces over local fields. I: Basic results on fractional integration
• p-adic models of ultrametric diffusion constrained by hierarchical energy landscapes

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