Published online by Cambridge University Press: 14 November 2011
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.