Journal of Operator Theory

Volume 51, Issue 1, Winter 2004 pp. 115-139.

Spectral problems for some indefinite cases of canonical differential equations

Authors: J. Rovnyak (1) and L.A. Sakhnovich (2)
Author institution: (1) University of Virginia, Department of Mathematics, Kerchof Hall, P. O. Box 400137, Charlottesville, VA 22904-4137, USA
(2) Visiting Member, Courant Institute of Mathematical Sciences. Address: 735 Crawford Avenue, Brooklyn, NY 11223, USA

Summary: The method of operator identities is used to investigate inverse problems of spectral theory for canonical systems of differential equations in some indefinite cases. The theory is extended in a different direction by including both the continuous and discrete cases at the same time. A generalization of the matrix string equation is obtained as an example.

Keywords: Canonical differential equation, inverse problem, spectral data, operator identity, string equation, Kre{\u\i}n space, Pontryagin space

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