4 papers
A Pseudo-Differential Operator of the -Adic Multiplicative Calculus
Alexandra V. Antoniouk, Anatoly N. Kochubei, Mariia V. Serdiuk
We introduce and study a pseudo-differential operator , defined via the -adic Mellin transformation, acting on real- or complex-valued functions on the multiplicative grou…
Monotonicity Property of Non-Archimedean Heat Equation
Alexandra V. Antoniouk, Anatoly N. Kochubei
We prove the monotone dependence of the heat kernel corresponding to the Vladimirov-Taibleson non-Archimedean fractional differentiation operator on the order .
Non-Archimedean Kelvin Transformation
Alexandra V. Antoniouk, Anatoly N. Kochubei
We introduce and study an analog of the Kelvin transformation connected with the Vladimirov-Taibleson operator acting on real- or complex-valued functions on a space over a n…
Non-Archimedean Neumann problem: weak and strong solutions
Alexandra V. Antoniouk, Anatoly N. Kochubei
We consider the Neumann problem for the equation with the Vladimirov-Taibleson fractional differentiation operator over a non-Archimedean local field. We study weak solutions follo…