Ground-state positivity, negativity, and compactness for a Schrödinger operator in \(\mathbb R^N\)

DOI10.1016/j.jfa.2006.12.007zbMath1231.81036OpenAlexW2063437559MaRDI QIDQ880120

Peter Takáč, Bénédicte Alziary, Jacqueline Fleckinger-Pellé

Publication date: 10 May 2007

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2006.12.007

zbMATH Keywords

Schrödinger operatoranti-maximum principlecompact resolventground-state positivity and negativityRiesz-Schauder theoryWKB-type asymptotic formula

Mathematics Subject Classification ID

General theory of partial differential operators (47F05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) Algebras of operators on Banach spaces and other topological linear spaces (47L10)

Related Items

Positive solutions of Schrödinger equations in product form and Martin compactifications of the plane, Characterization of intrinsic ultracontractivity for one dimensional Schrödinger operators, Semi-linear cooperative elliptic systems involving Schr{\"o}dinger operators: Groundstate positivity or negativity, Intrinsic ultracontractivity of a Schrödinger semigroup in \(\mathbb R^N\), On weighted boundedness and compactness of operators generated by fractional heat semigroups related with Schrödinger operators

Cites Work

• A pointwise lower bound for positive solutions of a Schrödinger equation in \(\mathbb{R}^ N\)
• Strong positivity in \(C(\bar\Omega)\) for elliptic systems
• Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians
• An anti-maximum principle for second order elliptic operators
• An extension of maximum and anti-maximum principles to a Schrödinger equation in \(\mathbb{R}^2\)
• An abstract form of maximum and anti-maximum principles of Hopf's type
• A Remark on Bony Maximum Principle
• On the asymptotic decay of L²-solutions of one-body Schrödinger equations in unbounded domains
• Asymptotic Integrations of Linear Differential Equations
• Positivity and negativity of solutions to a Schrödinger equation in \(\mathbb{R}^N\).
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item