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Autor Israel Gohberg |
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Título : Factorization of Matrix and Operator Functions: The State Space Method Tipo de documento: documento electrónico Autores: Harm Bart ; SpringerLink (Online service) ; André C. M. Ran ; Israel Gohberg ; Marinus A. Kaashoek Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2008 Colección: Operator Theory: Advances and Applications, Linear Operators and Linear Systems num. 178 Número de páginas: XII, 412 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-8268-1 Idioma : Inglés (eng) Palabras clave: Mathematics Matrix theory Algebra Operator Number Theory Linear and Multilinear Algebras, Clasificación: 51 Matemáticas Resumen: The present book deals with factorization problems for matrix and operator functions. The problems originate from, or are motivated by, the theory of non-selfadjoint operators, the theory of matrix polynomials, mathematical systems and control theory, the theory of Riccati equations, inversion of convolution operators, theory of job scheduling in operations research. The book systematically employs a geometric principle of factorization which has its origins in the state space theory of linear input-output systems and in the theory of characteristic operator functions. This principle allows one to deal with different factorizations from one point of view. Covered are canonical factorization, minimal and non-minimal factorizations, pseudo-canonical factorization, and various types of degree one factorization. Considerable attention is given to the matter of stability of factorization which in terms of the state space method involves stability of invariant subspaces.invariant subspaces Nota de contenido: Motivating Problems, Systems and Realizations -- Motivating Problems -- Operator Nodes, Systems, and Operations on Systems -- Various Classes of Systems -- Realization and Linearization of Operator Functions -- Factorization and Riccati Equations -- Canonical Factorization and Applications -- Minimal Realization and Minimal Factorization -- Minimal Systems -- Minimal Realizations and Pole-Zero Structure -- Minimal Factorization of Rational Matrix Functions -- Degree One Factors, Companion Based Rational Matrix Functions, and Job Scheduling -- Factorization into Degree One Factors -- Complete Factorization of Companion Based Matrix Functions -- Quasicomplete Factorization and Job Scheduling -- Stability of Factorization and of Invariant Subspaces -- Stability of Spectral Divisors -- Stability of Divisors -- Factorization of Real Matrix Functions En línea: http://dx.doi.org/10.1007/978-3-7643-8268-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34386 Factorization of Matrix and Operator Functions: The State Space Method [documento electrónico] / Harm Bart ; SpringerLink (Online service) ; André C. M. Ran ; Israel Gohberg ; Marinus A. Kaashoek . - Basel : Birkhäuser Basel, 2008 . - XII, 412 p : online resource. - (Operator Theory: Advances and Applications, Linear Operators and Linear Systems; 178) .
ISBN : 978-3-7643-8268-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Matrix theory Algebra Operator Number Theory Linear and Multilinear Algebras, Clasificación: 51 Matemáticas Resumen: The present book deals with factorization problems for matrix and operator functions. The problems originate from, or are motivated by, the theory of non-selfadjoint operators, the theory of matrix polynomials, mathematical systems and control theory, the theory of Riccati equations, inversion of convolution operators, theory of job scheduling in operations research. The book systematically employs a geometric principle of factorization which has its origins in the state space theory of linear input-output systems and in the theory of characteristic operator functions. This principle allows one to deal with different factorizations from one point of view. Covered are canonical factorization, minimal and non-minimal factorizations, pseudo-canonical factorization, and various types of degree one factorization. Considerable attention is given to the matter of stability of factorization which in terms of the state space method involves stability of invariant subspaces.invariant subspaces Nota de contenido: Motivating Problems, Systems and Realizations -- Motivating Problems -- Operator Nodes, Systems, and Operations on Systems -- Various Classes of Systems -- Realization and Linearization of Operator Functions -- Factorization and Riccati Equations -- Canonical Factorization and Applications -- Minimal Realization and Minimal Factorization -- Minimal Systems -- Minimal Realizations and Pole-Zero Structure -- Minimal Factorization of Rational Matrix Functions -- Degree One Factors, Companion Based Rational Matrix Functions, and Job Scheduling -- Factorization into Degree One Factors -- Complete Factorization of Companion Based Matrix Functions -- Quasicomplete Factorization and Job Scheduling -- Stability of Factorization and of Invariant Subspaces -- Stability of Spectral Divisors -- Stability of Divisors -- Factorization of Real Matrix Functions En línea: http://dx.doi.org/10.1007/978-3-7643-8268-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34386 Ejemplares
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Título : Holomorphic Operator Functions of One Variable and Applications : Methods from Complex Analysis in Several Variables Tipo de documento: documento electrónico Autores: Israel Gohberg ; SpringerLink (Online service) ; Jürgen Leiterer Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2009 Colección: Operator Theory: Advances and Applications num. 192 Número de páginas: XX, 424 p Il.: online resource ISBN/ISSN/DL: 978-3-0346-0126-9 Idioma : Inglés (eng) Palabras clave: Mathematics Functions of complex variables Operator theory a Complex Variable Theory Clasificación: 51 Matemáticas Nota de contenido: Elementary properties of holomorphic functions -- Solution of and applications -- Splitting and factorization with respect to a contour -- The Rouché theorem for operator functions -- Multiplicative cocycles ( -cocycles) -- Families of subspaces -- Plemelj-Muschelishvili factorization -- Wiener-Hopf operators, Toeplitz operators and factorization -- Multiplicative cocycles with restrictions ( -cocycles) -- Generalized interpolation problems -- Holomorphic equivalence, linearization and diagonalization En línea: http://dx.doi.org/10.1007/978-3-0346-0126-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33999 Holomorphic Operator Functions of One Variable and Applications : Methods from Complex Analysis in Several Variables [documento electrónico] / Israel Gohberg ; SpringerLink (Online service) ; Jürgen Leiterer . - Basel : Birkhäuser Basel, 2009 . - XX, 424 p : online resource. - (Operator Theory: Advances and Applications; 192) .
ISBN : 978-3-0346-0126-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Functions of complex variables Operator theory a Complex Variable Theory Clasificación: 51 Matemáticas Nota de contenido: Elementary properties of holomorphic functions -- Solution of and applications -- Splitting and factorization with respect to a contour -- The Rouché theorem for operator functions -- Multiplicative cocycles ( -cocycles) -- Families of subspaces -- Plemelj-Muschelishvili factorization -- Wiener-Hopf operators, Toeplitz operators and factorization -- Multiplicative cocycles with restrictions ( -cocycles) -- Generalized interpolation problems -- Holomorphic equivalence, linearization and diagonalization En línea: http://dx.doi.org/10.1007/978-3-0346-0126-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33999 Ejemplares
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Título : Indefinite Linear Algebra and Applications Tipo de documento: documento electrónico Autores: Israel Gohberg ; SpringerLink (Online service) ; Peter Lancaster ; Leiba Rodman Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2005 Número de páginas: XII, 357 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-7350-4 Idioma : Inglés (eng) Palabras clave: Mathematics Matrix theory Algebra Operator Differential equations Theory Linear and Multilinear Algebras, Ordinary Equations Clasificación: 51 Matemáticas Resumen: This book is dedicated to relatively recent results in linear algebra with indefinite inner product. It also includes applications to differential and difference equations with symmetries, matrix polynomials and Riccati equations. These applications have been developed in the last fifty years, and all of them are based on linear algebra in spaces with indefinite inner product. The latter forms a new more or less independent branch of linear algebra and we gave it the name of indefinite linear algebra. This new subject in linear algebra is presented following the lines and principles of a standard linear algebra course. This book has the structure of a graduate text in which chapters of advanced linear algebra form the core. This together with the many significant applications and accessible style will make it widely useful for engineers, scientists and mathematicians alike Nota de contenido: and Outline -- Indefinite Inner Products -- Orthogonalization and Orthogonal Polynomials -- Classes of Linear Transformations -- Canonical Forms -- Real H-Selfadjoint Matrices -- Functions of H-Selfadjoint Matrices -- H-Normal Matrices -- General Perturbations. Stability of Diagonalizable Matrices -- Definite Invariant Subspaces -- Differential Equations of First Order -- Matrix Polynomials -- Differential and Difference Equations of Higher Order -- Algebraic Riccati Equations En línea: http://dx.doi.org/10.1007/b137517 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35335 Indefinite Linear Algebra and Applications [documento electrónico] / Israel Gohberg ; SpringerLink (Online service) ; Peter Lancaster ; Leiba Rodman . - Basel : Birkhäuser Basel, 2005 . - XII, 357 p : online resource.
ISBN : 978-3-7643-7350-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Matrix theory Algebra Operator Differential equations Theory Linear and Multilinear Algebras, Ordinary Equations Clasificación: 51 Matemáticas Resumen: This book is dedicated to relatively recent results in linear algebra with indefinite inner product. It also includes applications to differential and difference equations with symmetries, matrix polynomials and Riccati equations. These applications have been developed in the last fifty years, and all of them are based on linear algebra in spaces with indefinite inner product. The latter forms a new more or less independent branch of linear algebra and we gave it the name of indefinite linear algebra. This new subject in linear algebra is presented following the lines and principles of a standard linear algebra course. This book has the structure of a graduate text in which chapters of advanced linear algebra form the core. This together with the many significant applications and accessible style will make it widely useful for engineers, scientists and mathematicians alike Nota de contenido: and Outline -- Indefinite Inner Products -- Orthogonalization and Orthogonal Polynomials -- Classes of Linear Transformations -- Canonical Forms -- Real H-Selfadjoint Matrices -- Functions of H-Selfadjoint Matrices -- H-Normal Matrices -- General Perturbations. Stability of Diagonalizable Matrices -- Definite Invariant Subspaces -- Differential Equations of First Order -- Matrix Polynomials -- Differential and Difference Equations of Higher Order -- Algebraic Riccati Equations En línea: http://dx.doi.org/10.1007/b137517 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35335 Ejemplares
Signatura Medio Ubicación Sub-localización Sección Estado ningún ejemplar Interpolation, Schur Functions and Moment Problems / SpringerLink (Online service) ; Daniel Alpay ; Israel Gohberg (2006)
Título : Interpolation, Schur Functions and Moment Problems Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Daniel Alpay ; Israel Gohberg Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2006 Colección: Operator Theory: Advances and Applications, Linear Operators and Linear Systems num. 165 Número de páginas: XI, 304 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-7547-8 Idioma : Inglés (eng) Palabras clave: Mathematics Functional analysis Operator theory System Theory Systems Theory, Control Analysis Clasificación: 51 Matemáticas Resumen: Schur analysis originates with an 1917 article of Schur where he associated to a function, which is analytic and contractive in the open unit disk, a sequence, finite or infinite, of numbers in the open unit disk, called Schur coefficients. In signal processing, they are often named reflection coefficients. Under the word "Schur analysis" one encounters a variety of problems related to Schur functions, such as interpolation problems, moment problems, the study of the relationships between the Schur coefficients and the properties of the function, or the study of underlying operators. Such questions are also considered for some generalizations of Schur functions. Furthermore, there is an extension of the notion of a Schur function for functions that are analytic and have a positive real part in the open upper half-plane; these functions are called Carathéodory functions. This volume is almost entirely dedicated to the analysis of Schur and Carathéodory functions and to the solutions of problems for these classes Nota de contenido: Basic Boundary Interpolation for Generalized Schur Functions and Factorization of Rational J-unitary Matrix Functions -- Discrete Analogs of Canonical Systems with Pseudo-exponential Potential. Inverse Problems -- Boundary Nevanlinna—Pick Interpolation Problems for Generalized Schur Functions -- A Truncated Matricial Moment Problem on a Finite Interval -- Shift Operators Contained in Contractions, Schur Parameters and Pseudocontinuable Schur Functions -- The Matricial Carathéodory Problem in Both Nondegenerate and Degenerate Cases -- A Gohberg-Heinig Type Inversion Formula Involving Hankel Operators En línea: http://dx.doi.org/10.1007/3-7643-7547-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35019 Interpolation, Schur Functions and Moment Problems [documento electrónico] / SpringerLink (Online service) ; Daniel Alpay ; Israel Gohberg . - Basel : Birkhäuser Basel, 2006 . - XI, 304 p : online resource. - (Operator Theory: Advances and Applications, Linear Operators and Linear Systems; 165) .
ISBN : 978-3-7643-7547-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Functional analysis Operator theory System Theory Systems Theory, Control Analysis Clasificación: 51 Matemáticas Resumen: Schur analysis originates with an 1917 article of Schur where he associated to a function, which is analytic and contractive in the open unit disk, a sequence, finite or infinite, of numbers in the open unit disk, called Schur coefficients. In signal processing, they are often named reflection coefficients. Under the word "Schur analysis" one encounters a variety of problems related to Schur functions, such as interpolation problems, moment problems, the study of the relationships between the Schur coefficients and the properties of the function, or the study of underlying operators. Such questions are also considered for some generalizations of Schur functions. Furthermore, there is an extension of the notion of a Schur function for functions that are analytic and have a positive real part in the open upper half-plane; these functions are called Carathéodory functions. This volume is almost entirely dedicated to the analysis of Schur and Carathéodory functions and to the solutions of problems for these classes Nota de contenido: Basic Boundary Interpolation for Generalized Schur Functions and Factorization of Rational J-unitary Matrix Functions -- Discrete Analogs of Canonical Systems with Pseudo-exponential Potential. Inverse Problems -- Boundary Nevanlinna—Pick Interpolation Problems for Generalized Schur Functions -- A Truncated Matricial Moment Problem on a Finite Interval -- Shift Operators Contained in Contractions, Schur Parameters and Pseudocontinuable Schur Functions -- The Matricial Carathéodory Problem in Both Nondegenerate and Degenerate Cases -- A Gohberg-Heinig Type Inversion Formula Involving Hankel Operators En línea: http://dx.doi.org/10.1007/3-7643-7547-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35019 Ejemplares
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Título : Modern Analysis and Applications : The Mark Krein Centenary Conference Volume 1: Operator Theory and Related Topics Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Vadim M. Adamyan ; Israel Gohberg ; Anatoly Kochubei ; Gennadiy Popov ; Yurij Berezansky ; Myroslav Gorbachuk ; Valentyna Gorbachuk ; Heinz Langer Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2009 Colección: Operator Theory: Advances and Applications num. 190 Número de páginas: XXII, 490 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-9919-1 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Functional Integral equations Operator theory Theory Equations Clasificación: 51 Matemáticas Nota de contenido: Mark Grigorievich Krein (on his 100th birthday anniversary) -- Mark Grigorievich Krein (on his 100th birthday anniversary) -- Mark Grigorievich Krein (on his 100th birthday anniversary) -- Mark Grigorievich Krein (on his 100th birthday anniversary) -- Plenary Talks -- Modified Krein Formula and Analytic Perturbation Procedure for Scattering on Arbitrary Junction -- The Schur Transformation for Nevanlinna Functions: Operator Representations, Resolvent Matrices, and Orthogonal Polynomials -- M. Kre?n’s Research on Semi-Bounded Operators, its Contemporary Developments, and Applications -- Research Papers -- Remarks on the Inverse Spectral Theory for Singularly Perturbed Operators -- An Approach to a Generalization of White Noise Analysis -- Some Existence Conditions for the Compact Extrema of Variational Functionals of Several Variables in Sobolev Space W 2 1 -- The Moment Problem for Rational Measures: Convexity in the Spirit of Krein -- Almost Periodic Factorization of Some Triangular Matrix Functions -- On Generalized Operator-valued Toeplitz Kernels -- Abstract Interpolation Problem in Nevanlinna Classes -- On the Strong Kreiss Resolvent Condition in the Hilbert Space -- Anatomy of the C*-algebra Generated by Toeplitz Operators with Piece-wise Continuous Symbols -- Block Tridiagonal Matrices and a Beefed-up Version of the Ehrenfest Urn Model -- On The Unitarization Of Linear Representations Of Primitive Partially Ordered Sets -- Direct and Inverse Theorems in the Theory of Approximation of Banach Space Vectors by Exponential Type Entire Vectors -- Results on Convergence in Norm of Exponential Product Formulas and Pointwise of the Corresponding Integral Kernels -- Generalized Selfadjoint Operators -- Orthogonal Decomposition of Functions Subharmonic in the Unit Disc -- Asymptotics of Toeplitz Matrices with Symbols in Some Generalized Krein Algebras -- Generators of Random Processes in Ultrametric Spaces and Their Spectra -- On Pseudo-Hermitian Operators with Generalized C-symmetries -- Nonisospectral Flows on Self-adjoint, Unitary and Normal Semi-infinite Block Jacobi Matrices -- Compact Extrema: A General Theory and Its Applications to Variational Functionals -- On Extremal Problem for Algebraic Polynomials in Loading Spaces -- On Coxeter Graph Related Configurations of Subspaces of a Hilbert Space -- Correlation Functions of Intrinsically Stationary Random Fields -- Inverse Problem for Conservative Curved Systems En línea: http://dx.doi.org/10.1007/978-3-7643-9919-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34108 Modern Analysis and Applications : The Mark Krein Centenary Conference Volume 1: Operator Theory and Related Topics [documento electrónico] / SpringerLink (Online service) ; Vadim M. Adamyan ; Israel Gohberg ; Anatoly Kochubei ; Gennadiy Popov ; Yurij Berezansky ; Myroslav Gorbachuk ; Valentyna Gorbachuk ; Heinz Langer . - Basel : Birkhäuser Basel, 2009 . - XXII, 490 p : online resource. - (Operator Theory: Advances and Applications; 190) .
ISBN : 978-3-7643-9919-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Functional Integral equations Operator theory Theory Equations Clasificación: 51 Matemáticas Nota de contenido: Mark Grigorievich Krein (on his 100th birthday anniversary) -- Mark Grigorievich Krein (on his 100th birthday anniversary) -- Mark Grigorievich Krein (on his 100th birthday anniversary) -- Mark Grigorievich Krein (on his 100th birthday anniversary) -- Plenary Talks -- Modified Krein Formula and Analytic Perturbation Procedure for Scattering on Arbitrary Junction -- The Schur Transformation for Nevanlinna Functions: Operator Representations, Resolvent Matrices, and Orthogonal Polynomials -- M. Kre?n’s Research on Semi-Bounded Operators, its Contemporary Developments, and Applications -- Research Papers -- Remarks on the Inverse Spectral Theory for Singularly Perturbed Operators -- An Approach to a Generalization of White Noise Analysis -- Some Existence Conditions for the Compact Extrema of Variational Functionals of Several Variables in Sobolev Space W 2 1 -- The Moment Problem for Rational Measures: Convexity in the Spirit of Krein -- Almost Periodic Factorization of Some Triangular Matrix Functions -- On Generalized Operator-valued Toeplitz Kernels -- Abstract Interpolation Problem in Nevanlinna Classes -- On the Strong Kreiss Resolvent Condition in the Hilbert Space -- Anatomy of the C*-algebra Generated by Toeplitz Operators with Piece-wise Continuous Symbols -- Block Tridiagonal Matrices and a Beefed-up Version of the Ehrenfest Urn Model -- On The Unitarization Of Linear Representations Of Primitive Partially Ordered Sets -- Direct and Inverse Theorems in the Theory of Approximation of Banach Space Vectors by Exponential Type Entire Vectors -- Results on Convergence in Norm of Exponential Product Formulas and Pointwise of the Corresponding Integral Kernels -- Generalized Selfadjoint Operators -- Orthogonal Decomposition of Functions Subharmonic in the Unit Disc -- Asymptotics of Toeplitz Matrices with Symbols in Some Generalized Krein Algebras -- Generators of Random Processes in Ultrametric Spaces and Their Spectra -- On Pseudo-Hermitian Operators with Generalized C-symmetries -- Nonisospectral Flows on Self-adjoint, Unitary and Normal Semi-infinite Block Jacobi Matrices -- Compact Extrema: A General Theory and Its Applications to Variational Functionals -- On Extremal Problem for Algebraic Polynomials in Loading Spaces -- On Coxeter Graph Related Configurations of Subspaces of a Hilbert Space -- Correlation Functions of Intrinsically Stationary Random Fields -- Inverse Problem for Conservative Curved Systems En línea: http://dx.doi.org/10.1007/978-3-7643-9919-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34108 Ejemplares
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