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      Non-Archimedean pseudodifferential operators with variable coefficients and Feller Semigroups

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          Abstract

          In this article we study a large class of non-Archimedean pseudodifferential operators whose symbols are negative definite functions. We prove that these operators extend to generators of Feller semigroups. In order to study these operators, we introduce a new class of anisotropic Sobolev spaces, which are the natural domains for the operators considered here. We also study the Cauchy problem for certain pseudodifferential equations.

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          Author and article information

          Journal
          07 August 2017
          Article
          1708.02308
          0d34c9b5-fb05-47a6-b133-7c58ee50a725

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          Custom metadata
          43A35, 46S10, 47G30 (primary), 60J25 (secondary)
          math.PR

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