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
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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.
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