Subcriticality, positivity, and gaugeability of the Schrödinger operator

DOI10.1090/S0273-0979-1990-15965-8zbMath0744.35042MaRDI QIDQ4712588

Zhongxin Zhao

Publication date: 25 June 1992

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

restricted Kato class of potentials

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) PDEs in connection with quantum mechanics (35Q40) Schrödinger operator, Schrödinger equation (35J10)

Related Items (13)

Gaussian bounds for the fundamental solutions of \(\nabla(A\nabla u)+B\nabla u-u_ t=0\) ⋮ First eigenvalues and comparison of Green's functions for elliptic operators on manifolds or domains ⋮ Sharp decay estimates of \(L^q\)-norms for nonnegative Schrödinger heat semigroups ⋮ Geometric inequalities for manifolds with Ricci curvature in the Kato class ⋮ \(L^ p\) norms of non-critical Schrödinger semigroups ⋮ Global existence and local continuity of solutions for semilinear parabolic equations ⋮ Global asymptotic behavior of solutions of a semilinear parabolic equation ⋮ Sharp decay estimates in Lorentz spaces for nonnegative Schrödinger heat semigroups ⋮ On the existence of positive solutions of nonlinear elliptic equations -- a probabilistic potential theory approach ⋮ The 3G-inequality for general Schrödinger operators on Lipschitz domains ⋮ \(L^p\) norms of nonnegative Schrödinger heat semigroup and the large time behavior of hot spots ⋮ Decay Rate of L q Norms of Critical Schrödinger Heat Semigroups ⋮ On positivity, criticality, and the spectral radius of the shuttle operator for elliptic operators

Cites Work

• Unnamed Item
• Positive solutions and large time behaviors of Schrödinger semigroups, Simon's problem
• On critical and subcritical Sturm-Liouville operators
• Green function for Schrödinger operator and conditioned Feynman-Kac gauge
• Structure of positive solutions to \((-\Delta +V)u=0\) in \(R^ n\)
• Large time behavior of the \(L^ p\) norm of Schrödinger semigroups
• Conditional gauge with unbounded potential
• Conditional Gauge and Potential Theory for the Schrodinger Operator
• Kac functional and Schrödinger equation

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