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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Albeverio, S., Khrennikov, A. & Shelkovich, V. Harmonic Analysis in the p-Adic Lizorkin Spaces: Fractional Operators, Pseudo-Differential Equations, p-Adic Wavelets, Tauberian Theorems. J Fourier Anal Appl 12, 393–425 (2006). https://doi.org/10.1007/s00041-006-6014-0
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DOI: https://doi.org/10.1007/s00041-006-6014-0