Document Type
Article
Publication Date
2002
Abstract
Realization theory for operator colligations on Pontryagin spaces is used to study interpolation and factorization in generalized Schur classes. Several criteria are derived which imply that a given function is almost the restriction of a generalized Schur function. The role of realization theory in coefficient problems is also discussed; a solution of an indefinite Carathéodory-Fejér problem is obtained, as well as a result that relates the number of negative (positive) squares of the reproducing kernels associated with the canonical coisometric, isometric, and unitary realizations of a generalized Schur function to the number of negative (positive) eigenvalues of matrices derived from their Taylor coefficients.
Recommended Citation
D. Alpay, T. Constantinescu, A. Dijksma and J. Rovnyak. A note on interpolation in the generalized Schur class. I. Applications of realization theory. Operator Theory: Advances and Applications, vol. 134 (2002) pp. 67-97.
Peer Reviewed
1
Copyright
Springer
Included in
Algebra Commons, Discrete Mathematics and Combinatorics Commons, Other Mathematics Commons
Comments
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Operator Theory: Advances and Applications, volume 134, in 2002 following peer review. The final publication is available at Springer via DOI: 10.1007/978-3-0348-8215-6_5