Friedrichs extension of operators defined by linear Hamiltonian systems on unbounded interval

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Authors	ŠIMON HILSCHER Roman ZEMÁNEK Petr
Year of publication	2010
Type	Article in Periodical
Magazine / Source	Mathematica Bohemica
MU Faculty or unit	Faculty of Science
Citation
Field	General mathematics
Keywords	Linear Hamiltonian system; Friedrichs extension; Self-adjoint operator; Recessive solution; Quadratic functional; Positivity; Conjoined basis
Attached files	Friedrichs_extension_of_operators_defined_by_linear_Hamiltonian_systems_on_unbounded_interval__Simon_Hilscher___Zemanek_.pdf
Description	In this paper we consider a linear operator on an unbounded interval associated with a matrix linear Hamiltonian system. We characterize its Friedrichs extension in terms of the recessive system of solutions at infinity. This generalizes a similar result obtained by Marletta and Zettl for linear operators defined by even-order Sturm--Liouville differential equations.
Related projects:	Mathematical structures and their physical applications Asymptotika, oscilace a kvadratické funkcionály v teorii dynamických rovnic Oscillation and spectral theory of differential and difference systems