Non-Archimedean pseudodifferential operators and Feller Semigroups
Probability
2017-12-06 v3
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.
Keywords
Cite
@article{arxiv.1708.02308,
title = {Non-Archimedean pseudodifferential operators and Feller Semigroups},
author = {Anselmo Torresblanca-Badillo and W. A. Zúñiga-Galindo},
journal= {arXiv preprint arXiv:1708.02308},
year = {2017}
}
Comments
Due to a calculation error, the results hold only for pseudodifferential equations "with constant coefficients"