Pseudodifferential Equations Over Non-Archimedean Spaces
Series: Lecture Notes in Mathematics; 2174;
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Product details:
- Edition number 1st ed. 2016
- Publisher Springer International Publishing
- Date of Publication 9 January 2017
- Number of Volumes 1 pieces, Book
- ISBN 9783319467375
- Binding Paperback
- No. of pages175 pages
- Size 235x155 mm
- Weight 3051 g
- Language English
- Illustrations XVI, 175 p. 1 illus. Illustrations, black & white 0
Categories
Long description:
Focusing on p-adic and adelic analogues of pseudodifferential equations, this monograph presents a very general theory of parabolic-type equations and their Markov processes motivated by their connection with models of complex hierarchic systems. The Gelfand-Shilov method for constructing fundamental solutions using local zeta functions is developed in a p-adic setting and several particular equations are studied, such as the p-adic analogues of the Klein-Gordon equation. Pseudodifferential equations for complex-valued functions on non-Archimedean local fields are central to contemporary harmonic analysis and mathematical physics and their theory reveals a deep connection with probability and number theory. The results of this book extend and complement the material presented by Vladimirov, Volovich and Zelenov (1994) and Kochubei (2001), which emphasize spectral theory and evolution equations in a single variable, and Albeverio, Khrennikov and Shelkovich (2010), which deals mainlywith the theory and applications of p-adic wavelets.
Table of Contents:
p-Adic Analysis: Essential Ideas and Results.- Parabolic-type Equations and Markov Processes.- Non-Archimedean Parabolic-type Equations With Variable Coefficients.- Parabolic-Type Equations on Adeles.- Fundamental Solutions and Schrödinger Equations.- Pseudodifferential Equations of Klein-Gordon Type.
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