Adelic multiresolution analysis, construction of wavelet bases and pseudo-differential operators

DOI10.1007/s00041-013-9304-3zbMath1311.42088OpenAlexW2066178541MaRDI QIDQ485207

Jan Harm van der Walt, Andrei Yu. Khrennikov, Vladimir Shelkovich

Publication date: 9 January 2015

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00041-013-9304-3

zbMATH Keywords

waveletsmultiresolution analysisfractional differentiation operatorpseudo-differential operatorsadeles

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Fractional derivatives and integrals (26A33) Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) Adèle rings and groups (11R56) Pseudodifferential operators (47G30)

Related Items (10)

\(p\)-adic mathematical physics: the first 30 years ⋮ Infinite series whose topology of convergence varies from point to point ⋮ Heat equations and wavelets on Mumford curves and their finite quotients ⋮ Solving nonlinear \(p\)-adic pseudo-differential equations: combining the wavelet basis with the Schauder fixed point theorem ⋮ \(p\)-adic wavelets and their applications ⋮ On the p-Adic analog of Richards’ equation with the finite difference method ⋮ On infinitesimal generators and Feynman–Kac integrals of adelic diffusion ⋮ Semicircular-like and semicircular laws on Banach \(*\)-probability spaces induced by dynamical systems of the finite adele ring \(A_{\mathbb{Q}}\) ⋮ On the solutions of Cauchy problem for two classes of semi-linear pseudo-differential equations over \(p\)-adic field ⋮ \(p\)-adic analogue of the wave equation

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