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

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

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

Analysis of PDEs 2026-07-25 v1

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

Abstract

We introduce and study a pseudo-differential operator $W^\alpha$ , defined via the $p$ -adic Mellin transformation, acting on real- or complex-valued functions on the multiplicative group of the field of $p$ -adic numbers. The operator $W^\alpha$ is maximally dissipative. An estimate of its heat kernel is given.

Keywords

p-adic numbers multiplicative group mellin transform pseudo-differential operator maximally dissipative heat kernel

Cite

@article{arxiv.2607.23256,
  title  = {A Pseudo-Differential Operator of the $p$-Adic Multiplicative Calculus},
  author = {Alexandra V. Antoniouk and Anatoly N. Kochubei and Mariia V. Serdiuk},
  journal= {arXiv preprint arXiv:2607.23256},
  year   = {2026}
}