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arXiv · 2607.23256

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

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

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Alexandra V. Antoniouk, Anatoly N. Kochubei, Mariia V. Serdiuk. 2026-07-25. A Pseudo-Differential Operator of the $p$-Adic Multiplicative Calculus. https://arxiv.org/abs/2607.23256

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