A formula on scattering length of positive smooth measures

Masayoshi Takeda

doi:10.1090/S0002-9939-09-10172-7

A formula on scattering length of positive smooth measures

Masayoshi Takeda

SCI - Mathematics

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

4 Citations (Scopus)

Abstract

M. Kac studied the scattering length probabilistically and conjectured that its semi-classical limit equals the capacity of the support of the potential. This conjecture has been proved independently by Taylor, Takahashi, and Tamura. In this paper we give another simple proof by the random time-change argument for Dirichlet forms and extend the previous results to positive measure potentials.

Original language	English
Pages (from-to)	1491-1494
Number of pages	4
Journal	Proceedings of the American Mathematical Society
Volume	138
Issue number	4
DOIs	https://doi.org/10.1090/S0002-9939-09-10172-7
Publication status	Published - 2010 Apr

Keywords

Dirichlet form
Scattering length
Symmetric Markov process
Time change

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9939-09-10172-7

Cite this

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abstract = "M. Kac studied the scattering length probabilistically and conjectured that its semi-classical limit equals the capacity of the support of the potential. This conjecture has been proved independently by Taylor, Takahashi, and Tamura. In this paper we give another simple proof by the random time-change argument for Dirichlet forms and extend the previous results to positive measure potentials.",

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KW - Dirichlet form

KW - Scattering length

KW - Symmetric Markov process

KW - Time change

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A formula on scattering length of positive smooth measures

Abstract

Keywords

ASJC Scopus subject areas

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