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Scattering Lengths for Additive Functionals and Their Semi-classical Asymptotics

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Dirichlet Forms and Related Topics (IWDFRT 2022)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 394))

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Abstract

Scattering lengths for positive additive functionals of symmetric Markov processes are studied. The additive functionals considered here are not necessarily continuous. After giving a systematic presentation of the fundamentals of the scattering length, we study the problems of semi-classical asymptotics for scattering length under relativistic stable processes, which extend previous results for the case of positive continuous additive functionals.

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Acknowledgements

The first named author was partially supported by JSPS KAKENHI Grant number 20K03635.

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Authors and Affiliations

  1. Faculty of Advanced Science and Technology, Kumamoto University, Kumamoto, 860-8555, Japan

    Daehong Kim

  2. National Institute of Technology, Kagoshima College, Kirishima, 899-5193, Japan

    Masakuni Matsuura

Authors
  1. Daehong Kim
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  2. Masakuni Matsuura
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Corresponding author

Correspondence to Daehong Kim .

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Editors and Affiliations

  1. Department of Mathematics, University of Washington, Seattle, WA, USA

    Zhen-Qing Chen

  2. Department of Mathematics, Kansai University, Osaka, Japan

    Masayoshi Takeda

  3. Department of Mathematics, Kansai University, Osaka, Japan

    Toshihiro Uemura

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Kim, D., Matsuura, M. (2022). Scattering Lengths for Additive Functionals and Their Semi-classical Asymptotics. In: Chen, ZQ., Takeda, M., Uemura, T. (eds) Dirichlet Forms and Related Topics. IWDFRT 2022. Springer Proceedings in Mathematics & Statistics, vol 394. Springer, Singapore. https://doi.org/10.1007/978-981-19-4672-1_14

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