MATHEMATICA BOHEMICA, Vol. 135, No. 2, pp. 209-222, 2010

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

Roman Simon Hilscher, Petr Zemanek

R. Simon Hilscher, P. Zemanek, Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlarska 2, CZ-611 37 Brno, Czech Republic, e-mail: hilscher@math.muni.cz, zemanek@math.muni.cz

Abstract: 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.

Keywords: linear Hamiltonian system, Friedrichs extension, self-adjoint operator, recessive solution, quadratic functional, positivity conjoined basis

Classification (MSC 2010): 47B25, 34L05, 34C10

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