#### 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