A remark on Kac’s scattering length formula

Fitzsimmons, P. J.; He, Ping; Ying, Jia

doi:10.1007/s11425-012-4546-0

Cited by 3 publications

(1 citation statement)

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“…The result in [22] was extended to a non-symmetric case by He [9]. For general right Markov processes, Fitzsimmons, He and Ying [7] extended Takahashi's result by using the tool of Kutznetsov measure and proved the analog of (1.1) for a positive continuous additive functional.…”

Section: Introductionmentioning

confidence: 95%

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

Kim

Matsuura

2019

Mathematische Nachrichten

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In this paper we study the scattering length for positive additive functionals of symmetric stable processes on ℝ . 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. K E Y W O R D Sadditive functionals, Dirichlet forms, scattering lengths, Schrödinger operators M S C ( 2 0 1 0 ) Primary: 47D08, 60J45; Secondary: 31C15, 60G52, 60J55 www.mn-journal.org

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Section: Introductionmentioning

confidence: 95%