The uncertainty principle lemma under gravity and the discrete spectrum of Schrödinger operators

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dc.creatorAkutagawa, Kazuo
dc.creatorKumura, Hironori
dc.date2008-12-26
dc.date2009-01-13
dc.date.accessioned2026-07-07T12:28:15Z
dc.date.available2026-07-07T12:28:15Z
dc.descriptionThe uncertainty principle lemma for the Laplacian on Euclidean spaces shows the borderline-behavior of a potential for the following question : whether the Schrödinger operator has a finite or infinite number of the discrete pectrum. In this paper, we will give a generalization of this lemma on Euclidean spaces to that on large classes of complete noncompact manifolds. Replacing Euclidean spaces by some specific classes of complete noncompact manifolds, including hyperbolic spaces, we also establish some criterions for the above-type question.
dc.description19 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/0812.4663
dc.identifierhttp://arxiv.org/abs/0812.4663
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/215476
dc.subjectDifferential Geometry
dc.subjectSpectral Theory
dc.subject58J50, 35J10
dc.titleThe uncertainty principle lemma under gravity and the discrete spectrum of Schrödinger operators
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