#### Title

### On the Class RSI of J-Contractive Functions Intertwining Solutions of Linear Differential Equations

#### Document Type

Article

#### Publication Date

2012

#### Abstract

In this paper we extend and solve in the class of functions RSI mentioned in the title, a number of problems originally set for the class RS of rational functions contractive in the open right-half plane, and unitary on the imaginary line with respect to some preassigned self-adjoint matrix. The problems we consider include the Schur algorithm, the partial realization problem and the Nevanlinna-Pick interpolation problem. The arguments rely on the one-to-one correspondence between elements in a given subclass of RSI and elements in RS. Another important tool in the arguments is a new result pertaining to the classical tangential Schur algorithm.

#### Recommended Citation

D. Alpay, A. Melnikov, and V. Vinnikov. On the class SI of J-contractive functions intertwining solutions of linear differential equations. Integral Equations and Operator Theory, vol. 74 (2012), no. 3, pp. 313-344.

#### 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

Integral Equations and Operator Theory, volume 74, in 2012 following peer review. The final publication is available at Springer via DOI: 10.1007/s00020-012-2002-8