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GREEN'S FUNCTIONS AND REGULARIZED TRACES OF STURM–LIOUVILLE OPERATORS ON GRAPHS

Published online by Cambridge University Press:  28 July 2008

Sonja Currie  and
Bruce A. Watson
Sonja Currie
Affiliation:
School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africa (sonja.currie@wits.ac.za; b.alastair.watson@gmail.com)
Bruce A. Watson
Affiliation:
School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africa (sonja.currie@wits.ac.za; b.alastair.watson@gmail.com)
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Abstract

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Asymptotic approximations to the Green's functions of Sturm–Liouville boundary-value problems on graphs are obtained. These approximations are used to study the regularized traces of the differential operators associated with these boundary-value problems. Various inverse spectral problems for Sturm–Liouville boundary-value problems on graphs resembling those considered in Halberg and Kramer's ‘A generalization of the trace concept' (Duke Mathematics Journal27 (1960), 607–617), for Sturm–Liouville problems, and Pielichowski's ‘An inverse spectral problem for linear elliptic differential operators' (Universitatis Iagellonicae Acta Mathematica27 (1988), 239–246), for elliptic boundary-value problems, are solved.

Keywords

Primary 47E0534L0534B45differential operatorsspectrumgraphs
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 51 , Issue 2 , June 2008 , pp. 315 - 335
Copyright
Copyright © Edinburgh Mathematical Society 2008