Softcover ISBN:  9780821807224 
Product Code:  CBMS/71 
List Price:  $33.00 
Individual Price:  $26.40 
Electronic ISBN:  9781470424312 
Product Code:  CBMS/71.E 
List Price:  $31.00 
Individual Price:  $24.80 

Book DetailsCBMS Regional Conference Series in MathematicsVolume: 71; 1989; 160 ppMSC: Primary 47; Secondary 30; 42; 46;
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 twosided tangential problems of both the NevanlinnaPick type and the CarathéodoryFejér 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.
Readership 
Table of Contents

Chapters

0. Notation and Preliminaries

1. $J$ Inner Functions

2. Reproducing Kernel Hilbert Spaces

3. Linear Fractional Transformations, Matrix Balls and More on Admissibility

4. More on $\mathcal {H}(U)$ Spaces

5. The NevanlinnaPick Problem

6. CarathéodoryFejér Interpolation

7. Singular Pick Matrices

8. The Lossless Inverse Scattering Problem

9. Nehari Interpolation

10. A Matrix Interpolation Problem

11. Maximum Entropy

13. Appendix on Positive Semidefinite Matrices


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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 twosided tangential problems of both the NevanlinnaPick type and the CarathéodoryFejér 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.

Chapters

0. Notation and Preliminaries

1. $J$ Inner Functions

2. Reproducing Kernel Hilbert Spaces

3. Linear Fractional Transformations, Matrix Balls and More on Admissibility

4. More on $\mathcal {H}(U)$ Spaces

5. The NevanlinnaPick Problem

6. CarathéodoryFejér Interpolation

7. Singular Pick Matrices

8. The Lossless Inverse Scattering Problem

9. Nehari Interpolation

10. A Matrix Interpolation Problem

11. Maximum Entropy

13. Appendix on Positive Semidefinite Matrices