Title: Krein-von Neumann and Friedrichs extensions for second order operators on time scales

Authors: Petr Zemanek

Addresses: Faculty of Science, Department of Mathematics and Statistics, Masaryk University, Kotlarska 2, CZ-61137 Brno, Czech Republic

Abstract: We consider an operator defined by the second order Sturm-Liouville equation on an unbounded time scale. For such an operator we give characterisations of the domains of its Krein-von Neumann and Friedrichs extensions by using the recessive solution. This generalises and unifies similar results obtained for operators connected with the second order Sturm-Liouville differential and difference equations.

Keywords: second order dynamic equations; time scales; Friedrichs extension; Krein-von Neumann extension; self-adjoint operators; recessive solution; quadratic functional; positivity.

DOI: 10.1504/IJDSDE.2011.038498

International Journal of Dynamical Systems and Differential Equations, 2011 Vol.3 No.1/2, pp.132 - 144

Published online: 09 Feb 2011 *

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