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arXiv · 1812.00041

Symbols of non-archimedean elliptic pseudo-differential operators, Feller semigroups, Markov transition function and negative definite functions

Ismael Gutiérrez García·Anselmo Torresblanca-Badillo
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Abstract

In this article we prove that the heat kernel attached to the non-archimedean elliptic pseudodifferential operators determine a Feller semigroup and a uniformly stochastically continuous C_0 transition function of some strong Markov processes X with state space (Q_p)^n. We explicitly write the Feller semigroup and the Markov transition function associated with the heat kernel. Also, we show that the symbols of these pseudo-differential operators are a negative definite function and moreover, that this symbols can be represented as a combination of a positive constant, a continuous homomorphism l : (Q_p)^n to R and a non-negative, continuous quadratic form q : (Q_p)^n to R.

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Ismael Gutiérrez García, Anselmo Torresblanca-Badillo. 2018-11-30. Symbols of non-archimedean elliptic pseudo-differential operators, Feller semigroups, Markov transition function and negative definite functions. https://arxiv.org/abs/1812.00041

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