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This book is dedicated to the memory of an outstanding mathematician and personality, Vladimir Petrovich Potapov, who made important contributions to and exerted considerable influence in the areas of operator theory, complex analysis and their points of juncture. The book commences with insightful biographical material, and then presents a collection of papers on different aspects of operator theory and complex analysis covering those recent achievements of the Odessa-Kharkov school in which Potapov was very active. The papers deal with interrelated problems and methods. The main topics are the multiplicative structure of contractive matrix and operator functions, operators in spaces with indefinite scalar products, inverse problems for systems of differential equations, interpolation and approximation problems for operator and matrix functions. The book will appeal to a wide group of mathematicians and engineers, and much of the material can be used for advanced courses and seminars.




This book is dedicated to the memory of an outstanding mathematician and personality, Vladimir Petrovich Potapov, who made important contributions to and exerted considerable influence in the areas of operator theory, complex analysis and their points of juncture. The book commences with insightful biographical material, and then presents a collection of papers on different aspects of operator theory and complex analysis covering those recent achievements of the Odessa-Kharkov school in which Potapov was very active. The papers deal with interrelated problems and methods. The main topics are the multiplicative structure of contractive matrix and operator functions, operators in spaces with indefinite scalar products, inverse problems for systems of differential equations, interpolation and approximation problems for operator and matrix functions. The book will appeal to a wide group of mathematicians and engineers, and much of the material can be used for advanced courses and seminars.




This book is dedicated to the memory of an outstanding mathematician and personality, Vladimir Petrovich Potapov, who made important contributions to and exerted considerable influence in the areas of operator theory, complex analysis and their points of juncture. The book commences with insightful biographical material, and then presents a collection of papers on different aspects of operator theory and complex analysis covering those recent achievements of the Odessa-Kharkov school in which Potapov was very active. The papers deal with interrelated problems and methods. The main topics are the multiplicative structure of contractive matrix and operator functions, operators in spaces with indefinite scalar products, inverse problems for systems of differential equations, interpolation and approximation problems for operator and matrix functions. The book will appeal to a wide group of mathematicians and engineers, and much of the material can be used for advanced courses and seminars.


Content:
Front Matter....Pages I-XXVIII
The Influence of V.P. Potapov and M.G. Kre?n on My Scientific Work....Pages 1-16
The Development of Some of V.P. Potapov’s Ideas the Geometric Theory of Operators in Spaces with Indefinite Metric....Pages 17-27
On the Potapov Theory of Multiplicative Representations....Pages 28-47
An Operator Approach to the Potapov Scheme for the Solution of Interpolation Problems....Pages 48-86
Description of a Class of Functions which Admit an Approximation by Rational Functions with Preassigned Poles I....Pages 87-132
An Analysis and Extension of V.P. Potapov’s Approach to Interpolation Problems with Applications to the Generalized Bi-Tangential Schur-Nevanlinna-Pick Problem and J-Inner-Outer Factorization....Pages 133-161
On the Theory of Inverse Problems for the Canonical Differential Equation....Pages 162-170
Some Properties of Linear-Fractional Transformations and the Harmonic Mean of Matrix Functions....Pages 171-184
Modification of V.P. Potapov’s Scheme in the Indefinite Case....Pages 185-201
Inverse problems for equations systems....Pages 202-211
Back Matter....Pages 212-212


This book is dedicated to the memory of an outstanding mathematician and personality, Vladimir Petrovich Potapov, who made important contributions to and exerted considerable influence in the areas of operator theory, complex analysis and their points of juncture. The book commences with insightful biographical material, and then presents a collection of papers on different aspects of operator theory and complex analysis covering those recent achievements of the Odessa-Kharkov school in which Potapov was very active. The papers deal with interrelated problems and methods. The main topics are the multiplicative structure of contractive matrix and operator functions, operators in spaces with indefinite scalar products, inverse problems for systems of differential equations, interpolation and approximation problems for operator and matrix functions. The book will appeal to a wide group of mathematicians and engineers, and much of the material can be used for advanced courses and seminars.


Content:
Front Matter....Pages I-XXVIII
The Influence of V.P. Potapov and M.G. Kre?n on My Scientific Work....Pages 1-16
The Development of Some of V.P. Potapov’s Ideas the Geometric Theory of Operators in Spaces with Indefinite Metric....Pages 17-27
On the Potapov Theory of Multiplicative Representations....Pages 28-47
An Operator Approach to the Potapov Scheme for the Solution of Interpolation Problems....Pages 48-86
Description of a Class of Functions which Admit an Approximation by Rational Functions with Preassigned Poles I....Pages 87-132
An Analysis and Extension of V.P. Potapov’s Approach to Interpolation Problems with Applications to the Generalized Bi-Tangential Schur-Nevanlinna-Pick Problem and J-Inner-Outer Factorization....Pages 133-161
On the Theory of Inverse Problems for the Canonical Differential Equation....Pages 162-170
Some Properties of Linear-Fractional Transformations and the Harmonic Mean of Matrix Functions....Pages 171-184
Modification of V.P. Potapov’s Scheme in the Indefinite Case....Pages 185-201
Inverse problems for equations systems....Pages 202-211
Back Matter....Pages 212-212
....
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