A formula on scattering length of dual Markov processes

He, Ping

doi:10.1090/s0002-9939-2010-10618-4

Cited by 4 publications

(1 citation statement)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For symmetric Markov processes again, Takeda [22] considered the behaviour of the scattering length of a positive smooth measure potential by using the random time change argument for Dirichlet forms and gave a simple elegant proof of the analog of (1.1) without Kac's regularity. 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: 93%

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

Kim

Matsuura

2019

Mathematische Nachrichten

View full text Add to dashboard Cite

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

show abstract