Partially Specified Matrices and Operators: Classification, Completion, Applications by Israel Gohberg
This book is devoted to a new direction in linear algebra and operator theory that deals with the invariants of partially specified matrices and operators, and with the spectral analysis of their completions. The theory developed centers around two major problems concerning matrices of which part of the entries are given and the others are unspecified. The first is a classification problem and aims at a simplification of the given part with the help of admissible similarities. The results here may be seen as a far reaching generalization of the Jordan canonical form. The second problem is called the eigenvalue completion problem and asks to describe all possible eigenvalues and their multiplicities of the matrices which one obtains by filling in the unspecified entries. Both problems are also considered in an infinite dimensional operator framework. A large part of the book deals with applications to matrix theory and analysis, namely to stabilization problems in mathematical system theory, to problems of Wiener-Hopf factorization and interpolation for matrix polynomials and rational matrix functions, to the Kronecker structure theory of linear pencils, and to non- everywhere defined operators. The eigenvalue completion problem has a natural associated inverse, which appears as a restriction problem. The analysis of these two problems is often simpler when a solution of the corresponding classification problem is available.-
Pseudo-Differential Operators and Generalized Functions
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Characteristic Functions, Scattering Functions and Transfer Functions
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The Characteristic Operator Function and Related Topics
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Ritt Operators and Their Functional Calculus
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The Wonders of the Cesàro Operator
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Harmonic Analysis Techniques for Elliptic Operators
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Integral Operators in Non-Standard Function Spaces
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Discrete and Continuous Models in the Theory of Networks
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Mathematical Results in Quantum Mechanics
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Contributions to Operator Theory and Its Applications
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Operator Extensions, Interpolation of Functions and Related Topics
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New Aspects in Interpolation and Completion Theories
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Toeplitz Operators and Related Topics
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Matrix and Operator Valued Functions
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Operator Calculus and Spectral Theory
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One-dimensional Linear Singular Integral Equations
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Quaternionic Closed Operators, Fractional Powers and Fractional Diffusion Processes
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Completeness Theorems and Characteristic Matrix Functions
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Operator Algebras, Toeplitz Operators and Related Topics
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Recent Developments in Operator Theory, Mathematical Physics and Complex Analysis
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Conservative Realizations of Herglotz-Nevanlinna Functions
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Pseudo-Differential Operators: Analysis, Applications and Computations
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Achievements and Challenges in the Field of Convolution Operators
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Elementary Operators and Their Applications
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A Panorama of Modern Operator Theory and Related Topics
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From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory
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Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations
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Linear Systems, Signal Processing and Hypercomplex Analysis
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Operator Methods in Mathematical Physics
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Spectral Theory and Analysis
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Recent Progress in Operator Theory and Its Applications
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Toeplitz Operators and Random Matrices
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Advances in Structured Operator Theory and Related Areas
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Periodic Differential Operators
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Advances in Harmonic Analysis and Operator Theory
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Weights, Extrapolation and the Theory of Rubio de Francia
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Mathematical Methods in Systems, Optimization, and Control
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Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation
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Levy Processes, Integral Equations, Statistical Physics: Connections and Interactions
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Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics
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M.G.Krein's Lectures on Entire Operators
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Schur Functions, Operator Colligations and Reproducing Kernel Pontryagin Spaces
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Nonselfadjoint Operators and Related Topics
| SKU | Unavailable |
| ISBN 13 | 9783034899062 |
| ISBN 10 | 3034899068 |
| Title | Partially Specified Matrices and Operators: Classification, Completion, Applications |
| Author | Israel Gohberg |
| Series | Operator Theory: Advances And Applications |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Springer Basel |
| Year published | 2011-09-19 |
| Number of pages | 368 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |