On a Lie group G, we investigate the discreteness of the spectrum of Schrödinger 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.

Schrödinger operators on Lie groups with purely discrete spectrum / T. Bruno, M. Calzi. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - 404:(2022), pp. 108444.1-108444.45. [10.1016/j.aim.2022.108444]

Schrödinger operators on Lie groups with purely discrete spectrum

T. Bruno
Primo
;
M. Calzi
Ultimo
2022

Abstract

On a Lie group G, we investigate the discreteness of the spectrum of Schrödinger 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.
Discrete spectrum; Lie groups; Muckenhoupt weights; Schrödinger operators
Settore MAT/05 - Analisi Matematica
2022
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/927119
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