The spectrum of Schrödinger operators with positive potentials in Riemannian manifolds

Zhongwei Shen

doi:10.1090/S0002-9939-03-06968-5

The spectrum of Schrödinger operators with positive potentials in Riemannian manifolds

Zhongwei Shen

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

Let M be a noncompact complete Riemannian manifold. We consider the Schrödinger operator -Δ + V acting on L²(M), where V is a non-negative, locally integrable function on M. We obtain some simple conditions which imply that inf Spec(-Δ + V), the bottom of the spectrum of -Δ + V, is strictly positive. We also establish upper and lower bounds for the counting function N(λ).

Original language	English
Pages (from-to)	3447-3456
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	131
Issue number	11
DOIs	https://doi.org/10.1090/S0002-9939-03-06968-5
State	Published - Nov 2003

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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title = "The spectrum of Schr{\"o}dinger operators with positive potentials in Riemannian manifolds",

abstract = "Let M be a noncompact complete Riemannian manifold. We consider the Schr{\"o}dinger operator -Δ + V acting on L2(M), where V is a non-negative, locally integrable function on M. We obtain some simple conditions which imply that inf Spec(-Δ + V), the bottom of the spectrum of -Δ + V, is strictly positive. We also establish upper and lower bounds for the counting function N(λ).",

author = "Zhongwei Shen",

year = "2003",

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doi = "10.1090/S0002-9939-03-06968-5",

language = "English",

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T1 - The spectrum of Schrödinger operators with positive potentials in Riemannian manifolds

AU - Shen, Zhongwei

PY - 2003/11

Y1 - 2003/11

N2 - Let M be a noncompact complete Riemannian manifold. We consider the Schrödinger operator -Δ + V acting on L2(M), where V is a non-negative, locally integrable function on M. We obtain some simple conditions which imply that inf Spec(-Δ + V), the bottom of the spectrum of -Δ + V, is strictly positive. We also establish upper and lower bounds for the counting function N(λ).

AB - Let M be a noncompact complete Riemannian manifold. We consider the Schrödinger operator -Δ + V acting on L2(M), where V is a non-negative, locally integrable function on M. We obtain some simple conditions which imply that inf Spec(-Δ + V), the bottom of the spectrum of -Δ + V, is strictly positive. We also establish upper and lower bounds for the counting function N(λ).

UR - https://www.scopus.com/pages/publications/0142138335

UR - https://www.scopus.com/pages/publications/0142138335#tab=citedBy

U2 - 10.1090/S0002-9939-03-06968-5

DO - 10.1090/S0002-9939-03-06968-5

M3 - Article

AN - SCOPUS:0142138335

SN - 0002-9939

VL - 131

SP - 3447

EP - 3456

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 11

ER -

The spectrum of Schrödinger operators with positive potentials in Riemannian manifolds

Abstract

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