Non-Archimedean pseudodifferential operators and Feller Semigroups

2017/08/07 by Torresblanca-Badillo, Anselmo, Zúñiga-Galindo, W. A.
#43A35 #46S10 #47G30 (primary) #60J25 (secondary) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1708.02308

Abstract

In this article we study a 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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