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

A co-publication of the AMS and CBMS
Available Formats:
Softcover ISBN: 978-0-8218-0722-4
Product Code: CBMS/71
List Price: $33.00 Individual Price:$26.40
Electronic ISBN: 978-1-4704-2431-2
Product Code: CBMS/71.E
List Price: $31.00 Individual Price:$24.80
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List Price: $49.50 Click above image for expanded view$J$Contractive Matrix Functions, Reproducing Kernel Hilbert Spaces and Interpolation A co-publication of the AMS and CBMS Available Formats:  Softcover ISBN: 978-0-8218-0722-4 Product Code: CBMS/71  List Price:$33.00 Individual Price: $26.40  Electronic ISBN: 978-1-4704-2431-2 Product Code: CBMS/71.E  List Price:$31.00 Individual Price: $24.80 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$49.50
• Book Details

CBMS Regional Conference Series in Mathematics
Volume: 711989; 160 pp
MSC: 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 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.

• 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 Nevanlinna-Pick Problem
• 6. Carathéodory-Fejér 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
• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 711989; 160 pp
MSC: 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 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.

• 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 Nevanlinna-Pick Problem
• 6. Carathéodory-Fejér 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
Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.