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Green's matrix and the formula of Titchmarsh-Kodaira for singular left-definite canonical eigenvalue problems

Published online by Cambridge University Press:  14 November 2011

Bernd Schultze
Bernd Schultze
Affiliation:
Department of Mathematics, University of Essen
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Synopsis

The theory of singular left-definite canonical eigenvalue problems treated by Nieβen and Schneider in is generalized to arbitrary λ∈(ℂ\ℝ∪{0}. In this enlarged theory the Green's matrix of the problem is evaluated and a natural analogue of the Titchmarsh-Kodaira formula is proved. This formula permits the explicit computation of the spectral matrix playing the main role in the expansion theorems of this theory.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 83 , Issue 1-2 , 1979 , pp. 147 - 183
Copyright
Copyright © Royal Society of Edinburgh 1979

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