Limit point, strong limit point and Dirichlet conditions for Hamiltonian differential systems
Copyright policy )Limit point, strong limit point and Dirichlet conditions for Hamiltonian differential systems
AbstractThis paper deals with singular Hamiltonian differential systems. Three conditions on the asymptotic behavior or square integrability of their maximal domain functions at a singular end point are studied: the limit point condition, the strong limit point condition and the Dirichlet condition. The equivalence between the limit point and strong limit point conditions is established for a class of such systems, and for another class, the three conditions are shown to imply each other. As an application, two unified descriptions of the Friedrichs extension for some systems in the second class are obtained. A key feature of the descriptions is: they do not use the deficiency indices of the systems. Several illustrating examples are presented. In particular, two simple descriptions of the Friedrichs extension for a family of Schrödinger operators with singular potentials are achieved. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim
- Northwestern University United States
- Northern Illinois University United States
- Shandong Women’s University China (People's Republic of)
Schrödinger operator, strong limit point condition, limit point condition, Dirichlet condition, Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.), General spectral theory of ordinary differential operators, Hamiltonian differential systems, Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems, Weyl theory and its generalizations for ordinary differential equations, Friedrichs extension, singular potential
Schrödinger operator, strong limit point condition, limit point condition, Dirichlet condition, Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.), General spectral theory of ordinary differential operators, Hamiltonian differential systems, Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems, Weyl theory and its generalizations for ordinary differential equations, Friedrichs extension, singular potential
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).6 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!