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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
; | Date: |
16 Dec 2005 | Subject: | Mathematical Physics; General Mathematics | 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. | Source: | arXiv, math-ph/0512055 | Services: | Forum | Review | PDF | Favorites |
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