A variational formula for Dirichlet forms and existence of ground states

Masayoshi Takeda

doi:10.1016/j.jfa.2013.10.024

A variational formula for Dirichlet forms and existence of ground states

Masayoshi Takeda

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

Let L be the generator of a symmetric Markov process on a locally compact separable metric space, and μ a certain measure in the Kato class. Employing a variational formula for Dirichlet forms, we show the existence of a ground state of the time-changed operator -1μL or the Schrödinger-type operator -L+μ.

Original language	English
Pages (from-to)	660-675
Number of pages	16
Journal	Journal of Functional Analysis
Volume	266
Issue number	2
DOIs	https://doi.org/10.1016/j.jfa.2013.10.024
Publication status	Published - 2014 Jan 15

Keywords

Dirichlet form
Ground state
Symmetric Markov process
Variational formula

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2013.10.024

Cite this

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abstract = "Let L be the generator of a symmetric Markov process on a locally compact separable metric space, and μ a certain measure in the Kato class. Employing a variational formula for Dirichlet forms, we show the existence of a ground state of the time-changed operator -1μL or the Schr{\"o}dinger-type operator -L+μ.",

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AB - Let L be the generator of a symmetric Markov process on a locally compact separable metric space, and μ a certain measure in the Kato class. Employing a variational formula for Dirichlet forms, we show the existence of a ground state of the time-changed operator -1μL or the Schrödinger-type operator -L+μ.

KW - Dirichlet form

KW - Ground state

KW - Symmetric Markov process

KW - Variational formula

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JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

ER -

A variational formula for Dirichlet forms and existence of ground states

Abstract

Keywords

ASJC Scopus subject areas

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