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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A formula on scattering length of positive smooth measures


Author: Masayoshi Takeda
Journal: Proc. Amer. Math. Soc. 138 (2010), 1491-1494
MSC (2010): Primary 60J45, 60J55; Secondary 31C25
Published electronically: December 2, 2009
MathSciNet review: 2578543
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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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Additional Information

Masayoshi Takeda
Affiliation: Mathematical Institute, Tohoku University, Aoba, Sendai, 980-8578, Japan
Email: takeda@math.tohoku.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10172-7
PII: S 0002-9939(09)10172-7
Keywords: Scattering length, symmetric Markov process, Dirichlet form, time change
Received by editor(s): March 11, 2009
Received by editor(s) in revised form: August 19, 2009
Published electronically: December 2, 2009
Additional Notes: The author was supported in part by Grant-in-Aid for Scientific Research (No. 18340033 (B)), Japan Society for the Promotion of Science.
Communicated by: Richard C. Bradley
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.