Multidimensional ultrametric pseudodifferential equations |
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Authors: | S Albeverio S V Kozyrev |
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Institution: | 1. Institut für Angewandte Mathematik, Universit?t Bonn, Wegelerstra?e 6, D-53115, Bonn, Germany 2. Interdisziplin?res Zentrum für Komplexe Systeme, Universit?t Bonn, R?merstra?e 164, D-53117, Bonn, Germany 3. Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia
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Abstract: | We develop an analysis of wavelets and pseudodifferential operators on multidimensional ultrametric spaces which are defined
as products of locally compact ultrametric spaces. We introduce bases of wavelets, spaces of generalized functions and the
space D′0(X) of generalized functions on a multidimensional ultrametric space. We also consider some family of pseudodifferential operators
on multidimensional ultrametric spaces. The notions of Cauchy problem for ultrametric pseudodifferential equations and of
ultrametric characteristics are introduced. We prove an existence theorem and describe all solutions for the Cauchy problem
(an analog of the Kovalevskaya theorem). |
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