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p-Adic analysis in the Lizorkin type spaces: fractional operators, pseudo-differential equations and Tauberian theorems

S. Albeverio·A. Yu. Khrennikov·V. M. Shelkovich
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Abstract

In this paper the p -adic Lizorkin spaces of test functions and distributions are introduced, and multidimensional Vladimirov's and Taibleson's fractional operators are studied on these spaces. Since the p -adic Lizorkin spaces are invariant under the Vladimirov and Taibleson operators, they can play a key role in considerations related to fractional operator problems. A class of p -adic pseudo-differential operators in the Lizorkin spaces is also introduced and solutions of pseudo-differential equations are constructed. p -Adic multidimensional Tauberian theorems connected with fractional operators and pseudo-differential operators for the Lizorkin distributions are also proved.

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S. Albeverio, A. Yu. Khrennikov, V. M. Shelkovich. 2005-12-16. p-Adic analysis in the Lizorkin type spaces: fractional operators, pseudo-differential equations and Tauberian theorems. https://arxiv.org/abs/math-ph/0512055

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