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


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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Correspondence to 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).

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  • Sobolev Spaces
  • Pseudo-differential operators
  • Convolution kernel
  • Green function
  • m-dissipative operators
  • Heat kernel
  • Non-archimedean analysis