CBMS Regional Conference Series in Mathematics 1989; 160 pp; softcover Number: 71 ISBN10: 0821807226 ISBN13: 9780821807224 List Price: US$29 Member Price: US$23.20 All Individuals: US$23.20 Order Code: CBMS/71
 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  \(J\) inner functions
 Reproducing kernel Hilbert spaces
 Linear fractional transformations, matrix balls and more on admissibility
 More on \(\mathcal H(U)\) spaces
 The NevanlinnaPick problem
 CarathéodoryFejér interpolation
 Singular Pick matrices
 The lossless inverse scattering problem
 Nehari interpolation
 A matrix interpolation problem
 Maximum entropy
