Non-Archimedean Pseudodifferential Operators and Feller Semigroups |
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| Authors: | Anselmo Torresblanca-Badillo W A Zúñiga-Galindo |
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| Institution: | 1.Departamento de Matemáticas y Estádistica,Universidad del Norte,Barranquilla,Colombia;2.Departamento de Matemáticas, Unidad Querétaro, Libramiento Norponiente #2000, Fracc. Real de Juriquilla,Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional,Santiago de Querétaro,México |
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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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