A Panorama of Modern Operator Theory and Related Topics [electronic resource] : The Israel Gohberg Memorial Volume /
Dym, Harry.editor.
Kaashoek, Marinus A.editor.
Lancaster, Peter.editor.
Langer, Heinz.editor.
Lerer, Leonid.editor.
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.
Description based upon print version of record.
""A Panorama of Modern Operater Theory and Related Topics""; ""Contents""; ""Preface""; ""An Interpolation Problem for Functions with Values in a Commutative Ring""; ""1. Introduction""; ""2. The white noise space""; ""3. The ring R""; ""4. Analytic functions with values in R""; ""5. Nevanlinna-Pick Interpolation""; ""6. More general interpolation problem""; ""References""; ""Minimal and Maximal Invariant Spaces of Holomorphic Functions on Bounded Symmetric Domains""; ""1. Bounded symmetric domains and Jordan triples""; ""2. Hilbert spaces of holomorphic functions""
""3. Invariant Banach spaces of holomorphic functions""""4. Invariant Banach spaces of vector-valued holomorphic functions""; ""5. Minimal spaces for non-tube type domains""; ""References""; ""B-regular J-inner Matrix-valued Functions""; ""1. Introduction""; ""2. A unitary operator from H(U) onto H(U~)""; ""3. Some properties of the class UBR(J)""; ""4. Canonical systems with B-regular matrizants""; ""5. Direct and inverse monodromy problems""; ""6. Connections with the theory of characteristic functions""; ""7. de Branges spaces""; ""8. An example""; ""References""
""Canonical Transfer-function Realization for Schur-Agler-class Functions of the Polydisk""""1. Introduction""; ""1.1. The classical setting and the legacy of Israel Gohberg""; ""1.2. Extensions to several variables""; ""1.3. The plan of the paper""; ""2. Preliminaries""; ""3. Weakly coisometric realizations""; ""3.1. Characterization of left Agler decompositions""; ""3.2. Weakly coisometric versus coisometric c.f.m.â€?s""; ""4. Weakly isometric realizations""; ""5. Weakly unitary realizations""; ""References""; ""Spectral Regularity of Banach Algebras and Non-commutative Gelfand Theory""
""2. The domains ...., .... and .""""3. Weighted Bergman spaces over ...., ...., and .""; ""4. Polar-type coordinates in .""; ""5. The operators R0 and R""; ""6. Toeplitz operators with quasi-hyperbolic symbols""; ""7. Hyperbolic k-quasi-radial symbols""; ""8. Hyperbolic k-quasi-homogeneous functions""; ""9. Commutativity results""; ""Appendix""; ""References""; ""Canonical Models for Bi-isometries""; ""1. Introduction""; ""2. Preliminaries about commuting isometries""; ""3. Inductive construction of commuting isometries""; ""4. The structure of bi-isometries""
""5. Functional representation""
Includes bibliographical references.
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.
Gohberg, I. (Israel), 1928-2009.
Operator theory.
Functional analysis.
Functions of complex variables.
Matrix theory.
Algebra.
System theory.
Operator Theory.
Functional Analysis.
Several Complex Variables and Analytic Spaces.
Linear and Multilinear Algebras, Matrix Theory.
Systems Theory, Control.
Operator theory