A formula on scattering length of positive smooth measures

Masayoshi Takeda

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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 languageEnglish
Pages (from-to)1491-1494
Number of pages4
JournalProceedings of the American Mathematical Society
Issue number4
Publication statusPublished - 2010 Apr


  • Dirichlet form
  • Scattering length
  • Symmetric Markov process
  • Time change

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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