Author:
Torresblanca-Badillo Anselmo,Narváez Alfredo R. R.,López-González José
Abstract
AbstractTwo types of p-adic pseudo-differential operators (denoted, respectively, by $${\mathcal {T}}_{{\varvec{f}}_{1},{\varvec{f}}_{2}}^{l}$$
T
f
1
,
f
2
l
and $${\mathcal {J}}_{{\varvec{f}}_{1},{\varvec{f}}_{2}}^{\alpha }$$
J
f
1
,
f
2
α
) are introduced in this article. We will show that the operator $${\mathcal {T}}_{{\varvec{f}}_{1},{\varvec{f}}_{2}}^{l}$$
T
f
1
,
f
2
l
determines certain Feller semigroups and stochastic processes with state space the p-adic numbers. The second type of these operators (defined on a new class of p-adic Sobolev space) are connected with contraction semigroups and parabolic pseudo-differential equations.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
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