**CBMS Regional Conference Series in Mathematics**

Volume: 71;
1989;
160 pp;
Softcover

MSC: Primary 47;
Secondary 30; 42; 46

Print ISBN: 978-0-8218-0722-4

Product Code: CBMS/71

List Price: $31.00

Individual Price: $24.80

**Electronic ISBN: 978-1-4704-2431-2
Product Code: CBMS/71.E**

List Price: $31.00

Individual Price: $24.80

# $J$ Contractive Matrix Functions, Reproducing Kernel Hilbert Spaces and Interpolation

Share this page
*Harry Dym*

A co-publication of the AMS and CBMS

This book evolved from a set of lectures presented under the auspices of the Conference Board of Mathematical Sciences at the Case Institute of Technology in September 1984. The original objective of the lectures was to present an introduction to the theory and applications of \(J\) inner matrices. However, in revising the lecture notes for publication, the author began to realize that the spaces \({\mathcal H}(U)\) and \({\mathcal H}(S)\) are ideal tools for treating a large class of matrix interpolation problems including ultimately two-sided tangential problems of both the Nevanlinna-Pick type and the Carathéodory-Fejér type, as well as mixtures of these. Consequently, the lecture notes were revised to bring \({\mathcal H}(U)\) and \({\mathcal H}(S)\) to center stage. This monograph is the first systematic exposition of the use of these spaces for interpolation problems.

#### Table of Contents

# Table of Contents

## $J$ Contractive Matrix Functions, Reproducing Kernel Hilbert Spaces and Interpolation

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Table of Contents v6 free
- Preface vii8 free
- 0. Notation and Preliminaries 112 free
- 1. J Inner Functions 1324
- 2. Reproducing Kernel Hilbert Spaces 2334
- 3. Linear Fractional Transformations, Matrix Balls and More on Admissibility 4051
- 4. More on H (U) Spaces 4859
- 5. The Nevanlinna-Pick Problem 6071
- 6. Carathéodory-Fejér Interpolation 6980
- 7. Singular Pick Matrices 8293
- 8. The Lossless Inverse Scattering Problem 91102
- 9. Nehari Interpolation 105116
- 10. A Matrix Interpolation Problem 117128
- 11. Maximum Entropy 124135
- Appendix on Positive Semidefinite Matrices 134145
- References 139150
- Back Cover Back Cover1159