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Canonical systems of differential equations with self-adjoint interface conditions on graphs

Published online by Cambridge University Press:  12 July 2007

Henk de Snoo  and
Henrik Winkler
Henk de Snoo
Affiliation:
Department of Mathematics and Computing Science, University of Groningen, PO Box 800, 9700 AV Groningen, The Netherlands ([email protected])
Henrik Winkler
Affiliation:
Department of Mathematics and Computing Science, University of Groningen, PO Box 800, 9700 AV Groningen, The Netherlands ([email protected])
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Abstract

For n canonical systems of differential equations, the corresponding n copies of their domain (0, ∞) are thought of as a graph with vertex 0. An interface condition at 0 is given by a so-called Nevanlinna pair. Explicit formulae are deduced for the spectral representation of the corresponding underlying self-adjoint relation and the generalized Fourier transformation. Furthermore, results on compressions of the Fourier transformation to closed linear subspaces and the multiplicity of the eigenvalues if the spectrum is discrete are presented

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 135 , Issue 2 , April 2005 , pp. 297 - 315
Copyright
Copyright © Royal Society of Edinburgh 2005

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