Non-Archimedean Pseudodifferential Operators 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.

About the authors

Anselmo Torresblanca-Badillo

Departamento de Matemáticas y Estádistica

Author for correspondence.
Email: atorresblanca@uninorte.edu.co
Colombia, Km. 5 Vía Puerto Colombia, Barranquilla

W. A. Zúñiga-Galindo

Departamento de Matemáticas, Unidad Querétaro, Libramiento Norponiente #2000, Fracc. Real de Juriquilla

Email: atorresblanca@uninorte.edu.co
Mexico, Santiago de Querétaro, Qro., 76230

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