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Non-archimedean pseudo-differential operators on Sobolev spaces related to negative definite functions

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Abstract

In this article we study a large class of pseudo-differential operators on Sobolev spaces related to negative definite functions in the p-adic context and in arbitrary dimension. We show that these operators are m-dissipatives and generators of a strongly continuous contraction semigroup on the sobolev spaces mentioned above. Also, we study the convolution kernel, the Green function and the heat kernel attached to these operators. In addition, we study certain inhomogeneous equations and the Cauchy problem naturally associated to these operators.

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  1. Programa de Matemáticas, Universidad del Atlántico, Km. 7 Vía Puerto Colombia, Barranquilla, Colombia

    Anselmo Torresblanca-Badillo

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Torresblanca-Badillo, A. Non-archimedean pseudo-differential operators on Sobolev spaces related to negative definite functions. J. Pseudo-Differ. Oper. Appl. 12, 7 (2021). https://doi.org/10.1007/s11868-021-00385-z

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