A Panorama of Modern Operator Theory and Related Topics: The Israel Gohberg Memorial Volume

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Harry Dym, Marinus Kaashoek, Peter Lancaster, Heinz Langer, Leonid Lerer
Springer Science & Business Media, Feb 1, 2012 - Mathematics - 642 pages
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This book is dedicated to the memory of Israel Gohberg (1928–2009) – one of the great mathematicians of our time – who inspired innumerable fellow mathematicians and directed many students. The volume reflects the wide spectrum of Gohberg’s mathematical interests. It consists of more than 25 invited and peer-reviewed original research papers written by his former students, co-authors and friends. Included are contributions to single and multivariable operator theory, commutative and non-commutative Banach algebra theory, the theory of matrix polynomials and analytic vector-valued functions, several variable complex function theory, and the theory of structured matrices and operators. Also treated are canonical differential systems, interpolation, completion and extension problems, numerical linear algebra and mathematical systems theory.

 

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Contents

An Interpolation Problem for Functions with Values in a Commutative Ring
2
Minimal and Maximal Invariant Spaces of Holomorphic Functions on Bounded Symmetric Domains
19
Bregular Jinner Matrixvalued Functions
50
Canonical Transferfunction Realization for SchurAglerclass Functions of the Polydisk
75
Spectral Regularity of Banach Algebras and Noncommutative Gelfand Theory
123
Banach Algebras of Commuting Toeplitz Operators on the Unit Ball via the Quasihyperbolic Group
154
Canonical Models for Biisometries
177
Firstorder Trace Formulae for the Iterates of the FoxLi Operator
206
Bernstein Widths and Super Strictly Singular Inclusions
358
On Inversion of Certain Structured Linear Transformations Related to Block Toeplitz Matrices
377
The Inverse of a Twolevel Positive Definite Toeplitz Operator Matrix
387
Parametrizing Structure Preserving Transformations of Matrix Polynomials
403
A Review of Canonical Forms for Selfadjoint Matrix Polynomials
425
Linearization Factorization and the Spectral Compression of a Selfadjoint Analytic Operator Function Under the Condition VM
444
An Estimate for the Splitting of Holomorphic Cocycles One Variable
465
The Discrete Algebraic Riccati Equation and Hermitian Block Toeplitz Matrices
495

Factorization Versus Invertibility of Matrix Functions on Compact Abelian Groups
225
Banded Matrices Banded Inverses and Polynomial Representations for Semiseparable Operators
241
Description of HelsonSzegö Measures in Terms of the Schur Parameter Sequences of Associated Schur Functions
269
Divide and Conquer Method for Eigenstructure of Quasiseparable Matrices Using Zeroes of Rational Matrix Functions
298
An Identity Satisfied by Certain Orthogonal Vectorvalued Functions
329
Invertibility of Certain Fredholm Operators
345
On Cyclic and Nearly Cyclic Multiagent Interactions in the Plane
513
A Trace Formula for Differential Operators of Arbitrary Order
540
Jordan Structures and Lattices of Invariant Subspaces of Real Matrices
571
Pseudospectral Functions for Canonical Differential Systems II
583
Operator Identities for Subnormal Tuples of Operators
613
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About the author (2012)

Harry Dym is Professor Emeritus in the Department of Mathematics at the Weizmann Institute of Science in Israel. He has written more than 100 papers and this is his 5th book. Professor Dym is well know for his work in this area and his research interests are Operator Theory, Interpolation Theory, Inverse Problems and Classical Analysis.

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