On a scattering length for additive functionals and spectrum of fractional Laplacian with a non‐local perturbation

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  • Daehong Kim
    Graduate School of Science and Technology Kumamoto University Kumamoto 860‐8555 Japan
  • Masakuni Matsuura
    National Institute of Technology Kagoshima College Kirishima 899‐5193 Japan

書誌事項

公開日
2019-11-29
資源種別
journal article
権利情報
  • http://onlinelibrary.wiley.com/termsAndConditions#vor
DOI
  • 10.1002/mana.201800254
  • 10.48550/arxiv.1910.13064
公開者
Wiley

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<jats:title>Abstract</jats:title><jats:p>In this paper we study the scattering length for positive additive functionals of symmetric stable processes on . The additive functionals considered here are not necessarily continuous. We prove that the semi‐classical limit of the scattering length equals the capacity of the support of a certain measure potential, thus extend previous results for the case of positive continuous additive functionals. We also give an equivalent criterion for the fractional Laplacian with a measure valued non‐local operator as a perturbation to have purely discrete spectrum in terms of the scattering length, by considering the connection between scattering length and the bottom of the spectrum of Schrödinger operator in our settings.</jats:p>

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