Schrodinger operators on Lie groups with purely discrete spectrum

被引：0

作者：

Bruno, Tommaso ^{[1
,3
]}

Calzi, Mattia ^{[2
]}

机构：

[1] Univ Ghent, Dept Math Anal Log & Discrete Math, Krijgslaan 281, B-9000 Ghent, Belgium

[2] Univ Milan, Dipartimento Matemat, Via C Saldini 50, I-20133 Milan, Italy

[3] Univ Genoa, Dipartimento Matemat, Via Dodecaneso 35, I-16146 Genoa, Italy

来源：

ADVANCES IN MATHEMATICS | 2022年 / 404卷

基金：

比利时弗兰德研究基金会;

关键词：

Lie groups; Schrodinger operators; Discrete spectrum; Muckenhoupt weights; SUB-LAPLACIANS; HEAT KERNEL; SPACES; INEQUALITIES;

D O I：

10.1016/j.aim.2022.108444

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

On a Lie group G, we investigate the discreteness of the spectrum of Schrodinger operators of the form L + V, where L is a subelliptic sub-Laplacian on G and the potential V is a locally integrable function which is bounded from below. We prove general necessary and sufficient conditions for arbitrary potentials, and we obtain explicit characterizations when V is a polynomial on G or belongs to a local Muckenhoupt class. We finally discuss how to transfer our results to weighted sub-Laplacians on G. (c) 2022 Elsevier Inc. All rights reserved.

引用

页数：45

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