Damir Z. Arov's Books

Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems

By: Damir Z. Arov,Harry Dym

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Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems

By: Damir Z. Arov,Harry Dym

This monograph deals primarily with the prediction of vector valued stochastic processes that are either weakly stationary, or have weakly stationary increments, from finite segments of their past. The main focus is on the analytic counterpart of these problems, which amounts to computing projections onto subspaces of a Hilbert space of p x 1 vector valued functions with an inner product that is defined in terms of the p x p matrix valued spectral density of the process. The strategy is to identify these subspaces as vector valued de Branges spaces and then to express projections in terms of the reproducing kernels of these spaces and/or in terms of a generalized Fourier transform that is obtained from the solution of an associated inverse spectral problem. Subsequently, the projection of the past onto the future and the future onto the past is interpreted in terms of the range of appropriately defined Hankel operators and their adjoints, and, in the last chapter, assorted computations are carried out for rational spectral densities. The underlying mathematics needed to tackle this class of problems is developed in careful detail, but, to ease the reading, an attempt is made to avoid excessive generality. En route a number of results that, to the best of our knowledge, were only known for p = 1 are generalized to the case p > 1.

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Page Count

416

Publisher

Birkhäuser

Published Date

ISBN 10

3319702629

ISBN 13

9783319702629

Linear State/Signal Systems

By: Damir Z. Arov,Olof J. Staffans

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Linear State/Signal Systems

By: Damir Z. Arov,Olof J. Staffans

The authors explain in this work a new approach to observing and controlling linear systems whose inputs and outputs are not fixed in advance. They cover a class of linear time-invariant state/signal system that is general enough to include most of the standard classes of linear time-invariant dynamical systems, but simple enough that it is easy to understand the fundamental principles. They begin by explaining the basic theory of finite-dimensional and bounded systems in a way suitable for graduate courses in systems theory and control. They then proceed to the more advanced infinite-dimensional setting, opening up new ways for researchers to study distributed parameter systems, including linear port-Hamiltonian systems and boundary triplets. They include the general non-passive part of the theory in continuous and discrete time, and provide a short introduction to the passive situation. Numerous examples from circuit theory are used to illustrate the theory.

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Page Count

1050

Publisher

Cambridge University Press

Published Date

ISBN 10

1009021737

ISBN 13

9781009021739

Bitangential Direct and Inverse Problems for Systems of Integral and Differential Equations

By: Damir Z. Arov,Harry Dym

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Bitangential Direct and Inverse Problems for Systems of Integral and Differential Equations

By: Damir Z. Arov,Harry Dym

This largely self-contained treatment surveys, unites and extends some 20 years of research on direct and inverse problems for canonical systems of integral and differential equations and related systems. Five basic inverse problems are studied in which the main part of the given data is either a monodromy matrix; an input scattering matrix; an input impedance matrix; a matrix valued spectral function; or an asymptotic scattering matrix. The corresponding direct problems are also treated. The book incorporates introductions to the theory of matrix valued entire functions, reproducing kernel Hilbert spaces of vector valued entire functions (with special attention to two important spaces introduced by L. de Branges), the theory of J-inner matrix valued functions and their application to bitangential interpolation and extension problems, which can be used independently for courses and seminars in analysis or for self-study. A number of examples are presented to illustrate the theory.

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Page Count

487

Publisher

Cambridge University Press

Published Date

ISBN 10

1139560816

ISBN 13

9781139560818

J-Contractive Matrix Valued Functions and Related Topics

By: Damir Z. Arov,Harry Dym

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J-Contractive Matrix Valued Functions and Related Topics

By: Damir Z. Arov,Harry Dym

A comprehensive introduction to the theory of J-contractive and J-inner matrix valued functions with respect to the open upper half-plane and a number of applications of this theory. It will be of particular interest to those with an interest in operator theory and matrix analysis.

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Page Count

576

Publisher

Cambridge University Press

Published Date

ISBN 10

0521883008

ISBN 13

9780521883009

Linear State/Signal Systems

By: Damir Z. Arov,Olof J. Staffans

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Linear State/Signal Systems

By: Damir Z. Arov,Olof J. Staffans

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Page Count

1050

Publisher

Cambridge University Press

Published Date

ISBN 10

1009021737

ISBN 13

9781009021739

Bitangential Direct and Inverse Problems for Systems of Integral and Differential Equations

By: Damir Z. Arov,Harry Dym

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Bitangential Direct and Inverse Problems for Systems of Integral and Differential Equations

By: Damir Z. Arov,Harry Dym

An essentially self-contained treatment ideal for mathematicians, physicists or engineers whose research is connected with inverse problems.

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Page Count

487

Publisher

Cambridge University Press

Published Date

ISBN 10

1107018870

ISBN 13

9781107018877

Book's by Damir Z. Arov

Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems

Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems

Linear State/Signal Systems

Linear State/Signal Systems

Bitangential Direct and Inverse Problems for Systems of Integral and Differential Equations

Bitangential Direct and Inverse Problems for Systems of Integral and Differential Equations

J-Contractive Matrix Valued Functions and Related Topics

J-Contractive Matrix Valued Functions and Related Topics

Linear State/Signal Systems

Linear State/Signal Systems

Bitangential Direct and Inverse Problems for Systems of Integral and Differential Equations

Bitangential Direct and Inverse Problems for Systems of Integral and Differential Equations

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