On Order Isomorphisms Intertwining Semigroups for Dirichlet Forms

被引：0

作者：

Li, Liping ^{[1
,2
]}

Lin, Hanlai ^{[1
]}

机构：

[1] Fudan Univ, Sch Math Sci, Shanghai, Peoples R China

[2] Bielefeld Univ, Dept Math, Bielefeld, Germany

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2023年 / 36卷 / 02期

关键词：

Dirichlet forms; Order isomorphisms intertwining semigroups; h-transformations; Quasi-homeomorphisms; Irreducible decomposition; DIFFUSION DETERMINES;

D O I：

10.1007/s10959-022-01200-1

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

This paper is devoted to characterizing so-called order isomorphisms intertwining the L-2-semigroups of two quasi-regular Dirichlet forms. We first show that every unitary order isomorphism intertwining semigroups is the composition of h-transformation and quasi-homeomorphism. In addition, under the assumption that the underlying spaces admit so-called irreducible decompositions for Dirichlet forms, every (not necessarily unitary) order isomorphism intertwining semigroups can be expressed as the composition of h-transformation, quasi-homeomorphism and multiplication by a certain step function.

引用

页码：1304 / 1320

页数：17

共 15 条

[1]

Aliprantis CD., 2006, Positive operators

[2]

[Anonymous], 1992, Introduction to the theory of (nonsymmetric) Dirichlet forms

[3] Diffusion determines the manifold [J].

Arendt, W. ;

Biegert, M. ;

ter Elst, A. F. M. .

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2012, 667 :1-25

[4]

Arendt W, 2002, J REINE ANGEW MATH, V550, P97

[5]

Chen Z.-Q., 2012, London Mathematical Society Monographs Series

[6]

DelloSchiavo L., 2020, ARXIV

[7]

DelloSchiavo L., 2021, ARXIV

[8]

Fukushima M., 2011, DEGRUYTER STUDIES MA, V19

[9] ISOSPECTRAL PLANE DOMAINS AND SURFACES VIA RIEMANNIAN ORBIFOLDS [J].

GORDON, C ;

WEBB, D ;

WOLPERT, S .

INVENTIONES MATHEMATICAE, 1992, 110 (01) :1-22

[10] CAN ONE HEAR SHAPE OF A DRUM [J].

KAC, M .

AMERICAN MATHEMATICAL MONTHLY, 1966, 73 (4P2) :1-&

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