A. Kochubei

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math.AP2026

A Pseudo-Differential Operator of the $p$ -Adic Multiplicative Calculus

Alexandra V. Antoniouk, Anatoly N. Kochubei, Mariia V. Serdiuk

We introduce and study a pseudo-differential operator $W^{I^} \pm$ , defined via the $p$ -adic Mellin transformation, acting on real- or complex-valued functions on the multiplicative grou…

math.AP2026

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 $D^{I^} \pm$ on the order $I^\pm$ .

math.AP2025

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…

A Pseudo-Differential Operator of the p-Adic Multiplicative Calculus

Monotonicity Property of Non-Archimedean Heat Equation

Non-Archimedean Neumann problem: weak and strong solutions

A Pseudo-Differential Operator of the $p$ -Adic Multiplicative Calculus