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Self-adjoint extensions for singular linear Hamiltonian systems

✍ Scribed by Huaqing Sun; Yuming Shi

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
175 KB
Volume
284
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

This paper is concerned with self‐adjoint extensions for singular linear Hamiltonian systems. The domain of the closure of the corresponding minimal Hamiltonian operator is described by the properties of its elements at the endpoints of the discussed interval, and two different decompositions of the domain of the corresponding maximal Hamiltonian operator are provided. Based on them, complete and direct characterizations of all the self‐adjoint extensions for a Hamiltonian system are obtained in terms of square integrable solutions. As a consequence, the characterizations of all the self‐adjoint extensions are given for systems in the two special cases: the limit point case and limit circle case. Β© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim

πŸ“œ SIMILAR VOLUMES

Two singular point linear Hamiltonian sy
Two singular point linear Hamiltonian systems with an interface condition
✍ Horst Behncke; Don Hinton πŸ“‚ Article πŸ“… 2010 πŸ› John Wiley and Sons 🌐 English βš– 165 KB

## Abstract We consider the problem of a linear Hamiltionian system on ℝ with an interface condition which we take to be at __x__ = 0. Assuming limit point conditions at ±∞, we prove the problem is uniquely solvable, and a resolvent is constructed. Our method of solution is to map the problem onto