371 citations · 589 across the 56 of their papers we have counts for
62 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 group…
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…
Existence and uniqueness for -adic counterpart of the porous medium equation
Alexandra Antoniouk, Anatoly Kochubei, Oleksii Nikitchenko
We develop a theory of generalized solutions of the nonlinear evolution equations for complex-valued functions of a real positive time variable and -adic spatial variable, which…
The Vladimirov-Taibleson Operator: Inequalities, Dirichlet Problem, Boundary Hölder Regularity
Anatoly N. Kochubei
We study the Vladimirov-Taibleson operator, a model example of a pseudo-differential operator acting on real- or complex-valued functions defined on a non-Archimedean local field.…