Background
Dym, Harry was born on January 26, 1938 in Vienna, Austria. Son of Isaac and Anne (Hochman) Dym.
(This book evolved from a set of lectures presented under ...)
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 Caratheodory-Fejer 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.
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( This book deals with the relation between the past and ...)
This book deals with the relation between the past and the future of a real, one-dimensional, stationary Gaussian process. Kolmogorov and Wiener showed how best to predict the future knowing the whole past. The more difficult problem, when only a finite segment of the past is known, was solved by M. G. Krein. A full treatment of this problem, and the prerequisites for dealing with it, occupies most of the book. The first three chapters are devoted to the necessary background in function theory, Hardy spaces and probability. Later chapters introduce the spectral theory of a weighted string developed by Krein and certain Hilbert spaces of entire functions introduced by L. de Branges. Various other connections between past and future are considered, such as mixing and Markovian character. The final chapter treats the problem of interpolation, when the whole process is known except for a gap and it is desired to predict what happens there.
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(Linear algebra permeates mathematics, perhaps more so tha...)
Linear algebra permeates mathematics, perhaps more so than any other single subject. It plays an essential role in pure and applied mathematics, statistics, computer science, and many aspects of physics and engineering. This book conveys in a user-friendly way the basic and advanced techniques of linear algebra from the point of view of a working analyst. The techniques are illustrated by a wide sample of applications and examples that are chosen to highlight the tools of the trade. In short, this is material that many of us wish we had been taught as graduate students. Roughly the first third of the book covers the basic material of a first course in linear algebra. The remaining chapters are devoted to applications drawn from vector calculus, numerical analysis, control theory, complex analysis, convexity and functional analysis. In particular, fixed point theorems, extremal problems, matrix equations, zero location and eigenvalue location problems, and matrices with nonnegative entries are discussed. Appendices on useful facts from analysis and supplementary information from complex function theory are also provided for the convenience of the reader. In this new edition, most of the chapters in the first edition have been revised, some extensively. The revisions include changes in a number of proofs, either to simplify the argument, to make the logic clearer or, on occasion, to sharpen the result. New introductory sections on linear programming, extreme points for polyhedra and a Nevanlinna-Pick interpolation problem have been added, as have some very short introductory sections on the mathematics behind Google, Drazin inverses, band inverses and applications of SVD together with a number of new exercises.
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Dym, Harry was born on January 26, 1938 in Vienna, Austria. Son of Isaac and Anne (Hochman) Dym.
Bachelor of Electrical Engineering, Cooper Union, 1959. Master of Science in Electrical Engineering, California Institute of Technology, 1960. Doctor of Philosophy in Mathematics, Massachusetts Institute of Technology, 1965.
Communications engineer MITRE Corporation, Bedford, Massachusetts, 1960-1962. Instructor mathematics Massachusetts Institute of Technology, Cambridge, 1965-1966. Research associate Rockefeller University, New York City, 1966-1967.
Assistant professor City College of New York, 1968-1970. Senior scientist-professor mathematics Weizmann Institute of Science, Rehovot, Israel, since 1970.
(This book evolved from a set of lectures presented under ...)
( This book deals with the relation between the past and ...)
(Linear algebra permeates mathematics, perhaps more so tha...)
Member of Israeli Mathematics Society, American Mathematics Society.
Married Irene Lillian Rosner, May 26, 1959. Children: Jonathan, David, Michael.