Authors:
- Offers a fast introduction to the theory of pseudodifferential equations over non-Archimedean fields and their connections with mathematical physics, probability and number theory
- Provides a very general theory of parabolic-type equations and their Markov processes motivated by the models of hierarchic complex systems introduced by Avetisov et al. in around 2000
- Combines methods of PDEs, probability and number theory
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2174)
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Table of contents (7 chapters)
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Front Matter
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Back Matter
About this book
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.
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Authors and Affiliations
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Department of Mathematics, Center for Research and Advanced Studies of the National Polytechnic Institute (CINVESTAV), Mexico City, Mexico
W. A. Zúñiga-Galindo
Bibliographic Information
Book Title: Pseudodifferential Equations Over Non-Archimedean Spaces
Authors: W. A. Zúñiga-Galindo
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-46738-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Softcover ISBN: 978-3-319-46737-5Published: 09 January 2017
eBook ISBN: 978-3-319-46738-2Published: 08 January 2017
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XVI, 175
Number of Illustrations: 1 b/w illustrations
Topics: Abstract Harmonic Analysis, Functional Analysis, Mathematical Applications in the Physical Sciences, Number Theory, Probability Theory and Stochastic Processes, Mathematical Physics