全函数核代数上定义算子的Dirichlet问题

IF 0.3 Q4 MATHEMATICS

Acta Mathematica Vietnamica Pub Date : 2025-04-28 DOI:10.1007/s40306-025-00565-9

Sonia Chaari, Afef Ben Farah

{"title":"全函数核代数上定义算子的Dirichlet问题","authors":"Sonia Chaari, Afef Ben Farah","doi":"10.1007/s40306-025-00565-9","DOIUrl":null,"url":null,"abstract":"<div><p>This paper is devoted to the Dirichlet problem associated to operators defined on the nuclear algebra of entire functions. Firstly, we give a probabilistic representation of the solution of the Dirichlet problem associated to the extended <i>K</i>-Gross Laplacian in terms of <i>K</i>-Wiener process. Secondly, we prove that the Dirichlet problem associated to the operator <span>\\(\\mathcal {F}_{t(-K),I}\\)</span>-transform has an explicit solution. Finally, an application to the large deviation principle is given.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"50 2","pages":"159 - 172"},"PeriodicalIF":0.3000,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Dirichlet Problem Associated to Operators Defined on the Nuclear Algebra of Entire Functions\",\"authors\":\"Sonia Chaari, Afef Ben Farah\",\"doi\":\"10.1007/s40306-025-00565-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper is devoted to the Dirichlet problem associated to operators defined on the nuclear algebra of entire functions. Firstly, we give a probabilistic representation of the solution of the Dirichlet problem associated to the extended <i>K</i>-Gross Laplacian in terms of <i>K</i>-Wiener process. Secondly, we prove that the Dirichlet problem associated to the operator <span>\\\\(\\\\mathcal {F}_{t(-K),I}\\\\)</span>-transform has an explicit solution. Finally, an application to the large deviation principle is given.</p></div>\",\"PeriodicalId\":45527,\"journal\":{\"name\":\"Acta Mathematica Vietnamica\",\"volume\":\"50 2\",\"pages\":\"159 - 172\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2025-04-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica Vietnamica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40306-025-00565-9\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Vietnamica","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s40306-025-00565-9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

研究了在全函数的核代数上定义算子的狄利克雷问题。首先，我们用K-Wiener过程给出了与扩展K-Gross拉普拉斯算子相关的Dirichlet问题解的概率表示。其次，我们证明了与算子\(\mathcal {F}_{t(-K),I}\) -变换相关的Dirichlet问题有显式解。最后给出了大偏差原理的一个应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

The Dirichlet Problem Associated to Operators Defined on the Nuclear Algebra of Entire Functions

This paper is devoted to the Dirichlet problem associated to operators defined on the nuclear algebra of entire functions. Firstly, we give a probabilistic representation of the solution of the Dirichlet problem associated to the extended K-Gross Laplacian in terms of K-Wiener process. Secondly, we prove that the Dirichlet problem associated to the operator \(\mathcal {F}_{t(-K),I}\)-transform has an explicit solution. Finally, an application to the large deviation principle is given.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Acta Mathematica Vietnamica MATHEMATICS-

CiteScore

0.90

自引率

0.00%

发文量

期刊介绍： Acta Mathematica Vietnamica is a peer-reviewed mathematical journal. The journal publishes original papers of high quality in all branches of Mathematics with strong focus on Algebraic Geometry and Commutative Algebra, Algebraic Topology, Complex Analysis, Dynamical Systems, Optimization and Partial Differential Equations.