具有负定符号的新类 p-adic 伪微分算子及其应用

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Pseudo-Differential Operators and Applications Pub Date : 2024-09-07 DOI:10.1007/s11868-024-00616-z

Anselmo Torresblanca-Badillo, Edwin A. Bolaño-Benitez, Ismael Gutiérrez-García, Samuel Estala-Arias

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引用次数: 0

摘要

本文介绍了在特定条件下代表具有负定符号的 m 消散伪微分算子的新类 p-adic 算子。我们将研究与这些算子相关的新型半线性问题和马丁格尔问题，并将证明这些伪微分算子是 \(L^2({\mathbb {Q}}_p^n)\) 上强连续收缩半群的无穷小生成器。此外，本文还介绍了新的度量族、度量的解vent、正定度量、费勒半群和马尔可夫过程。

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New classes of p-adic pseudo-differential operators with negative definite symbols and their applications

This paper introduces new classes of p-adic operators representing m-dissipative pseudo-differential operators with negative definite symbols under certain conditions. We will study new types of semilinear problems and martingale problems associated with these operators, and we will prove that these pseudo-differential operators are the infinitesimal generators of strongly continuous contraction semigroups on \(L^2({\mathbb {Q}}_p^n)\). Also, this article introduces new families of measures, resolvent of measures, positive definite measures, Feller semigroups, and Markov processes.

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来源期刊

Journal of Pseudo-Differential Operators and Applications MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.20

自引率

9.10%

发文量

期刊介绍： The Journal of Pseudo-Differential Operators and Applications is a forum for high quality papers in the mathematics, applications and numerical analysis of pseudo-differential operators. Pseudo-differential operators are understood in a very broad sense embracing but not limited to harmonic analysis, functional analysis, operator theory and algebras, partial differential equations, geometry, mathematical physics and novel applications in engineering, geophysics and medical sciences.