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Pseudodifferential Equations Over Non-Archimedean Spaces (Paperback, 1st ed. 2016)
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Pseudodifferential Equations Over Non-Archimedean Spaces (Paperback, 1st ed. 2016)
Series: Lecture Notes in Mathematics, 2174
Expected to ship within 10 - 15 working days
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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 mainly with the theory and
applications of p-adic wavelets.
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