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Criticality and subcriticality of generalized Schrödinger forms with non-local perturbations


Author: Liping Li
Journal: Proc. Amer. Math. Soc. 145 (2017), 3929-3939
MSC (2010): Primary 31C25, 31C05, 60J25
DOI: https://doi.org/10.1090/proc/13523
Published electronically: February 15, 2017
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Abstract: In this paper, we shall treat the Schrödinger forms with non-local perturbations. We first extend the definitions of subcriticality, criticality and supercriticality for the Schrödinger forms by Takeda (2014) to the non-local cases in the context of quasi-regular Dirichlet forms. Then we prove an analytic characterization of these definitions via the bottom of the spectrum set.


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Additional Information

Liping Li
Affiliation: Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
Email: liping_li@amss.ac.cn

DOI: https://doi.org/10.1090/proc/13523
Received by editor(s): March 23, 2016
Received by editor(s) in revised form: September 20, 2016, and September 27, 2016
Published electronically: February 15, 2017
Additional Notes: This research was partially supported by a joint grant (No. 2015LH0043) of China Postdoctoral Science Foundation and Chinese Academy of Science, and China Postdoctoral Science Foundation (No. 2016M590145)
Communicated by: David Levin
Article copyright: © Copyright 2017 American Mathematical Society

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