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A formula on scattering length of positive smooth measures
Author(s):
Masayoshi
Takeda
Journal:
Proc. Amer. Math. Soc.
138
(2010),
1491-1494.
MSC (2010):
Primary 60J45, 60J55;
Secondary 31C25
Posted:
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.
References:
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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:
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
Posted:
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
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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