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Harmonic Analysis in the p-Adic Lizorkin Spaces: Fractional Operators, Pseudo-Differential Equations, p-Adic Wavelets, Tauberian Theorems |
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| Authors: | S Albeverio A Yu Khrennikov VM Shelkovich |
| Institution: | 1. Institut für Angewandte Mathematik, Universit?t Bonn Wegelerstra?e 6, D-53115 Bonn, Germany 2. International Center for Mathematical Modelling in Physics and Cognitive Sciences MSI, V?xj? University, SE-351 95, V?xj?, Sweden 3. Department of Mathematics, St.-Petersburg State University of Architecture and Civil Engineering, 2-ja Krasnoarmejskaja 4, 190005, St. Petersburg, Russia |
| Abstract: | In this article the p-adic Lizorkin spaces of test functions and distributions are introduced. Multi-dimensional Vladimirov’s and Taibleson’s fractional operators, and a class of p-adic pseudo-differential operators are studied on these spaces. Since the p-adic Lizorkin spaces are invariant under these operators, they can play a key role in considerations related to fractional operator problems. Solutions of pseudo-differential equations are also constructed. Some problems of spectral analysis of pseudo-differential operators are studied. p-Adic multidimensional Tauberian theorems connected with these pseudo-differential operators for the Lizorkin distributions are proved. |
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