Quaternionic de Branges Spaces and Characteristic Operator Function, Daniel Alpay; Fabrizio Colombo; Irene Sabadini

Автор: Colombo Fabrizio, Gantner Jonathan
Название: Quaternionic Closed Operators, Fractional Powers and Fractional Diffusion Processes
ISBN: 303016411X ISBN-13(EAN): 9783030164119
Издательство: Springer
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Цена: 79190.00 T
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Описание: This book presents a new theory for evolution operators and a new method for defining fractional powers of vector operators.

Автор: Damir Z. Arov; Harry Dym
Название: Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems
ISBN: 3319702610 ISBN-13(EAN): 9783319702612
Издательство: Springer
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Цена: 102480.00 T
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Описание: 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.

Автор: Sorin G. Gal; Irene Sabadini
Название: Quaternionic Approximation
ISBN: 3030106640 ISBN-13(EAN): 9783030106645
Издательство: Springer
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Цена: 51230.00 T
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Описание: This book presents the extensions to the quaternionic setting of some of the main approximation results in complex analysis. It also includes the main inequalities regarding the behavior of the derivatives of polynomials with quaternionic cofficients. With some few exceptions, all the material in this book belongs to recent research of the authors on the approximation of slice regular functions of a quaternionic variable. The book is addressed to researchers in various areas of mathematical analysis, in particular hypercomplex analysis, and approximation theory. It is accessible to graduate students and suitable for graduate courses in the above framework.

Автор: Fabrizio Colombo; Jonathan Gantner
Название: Quaternionic Closed Operators, Fractional Powers and Fractional Diffusion Processes
ISBN: 303016408X ISBN-13(EAN): 9783030164089
Издательство: Springer
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Цена: 93160.00 T
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Описание: This book presents a new theory for evolution operators and a new method for defining fractional powers of vector operators. This new approach allows to define new classes of fractional diffusion and evolution problems. These innovative methods and techniques, based on the concept of S-spectrum, can inspire researchers from various areas of operator theory and PDEs to explore new research directions in their fields.This monograph is the natural continuation of the book: Spectral Theory on the S-Spectrum for Quaternionic Operators by Fabrizio Colombo, Jonathan Gantner, and David P. Kimsey (Operator Theory: Advances and Applications, Vol. 270).

Автор: Fabrizio Colombo; Jonathan Gantner; David P. Kimse
Название: Spectral Theory on the S-Spectrum for Quaternionic Operators
ISBN: 3030030733 ISBN-13(EAN): 9783030030735
Издательство: Springer
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Цена: 79190.00 T
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Описание: The subject of this monograph is the quaternionic spectral theory based on the notion of S-spectrum. With the purpose of giving a systematic and self-contained treatment of this theory that has been developed in the last decade, the book features topics like the S-functional calculus, the F-functional calculus, the quaternionic spectral theorem, spectral integration and spectral operators in the quaternionic setting. These topics are based on the notion of S-spectrum of a quaternionic linear operator. Further developments of this theory lead to applications in fractional diffusion and evolution problems that will be covered in a separate monograph.

Автор: Daniel Alpay; Victor Vinnikov
Название: Characteristic Functions, Scattering Functions and Transfer Functions
ISBN: 3034601824 ISBN-13(EAN): 9783034601825
Издательство: Springer
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Цена: 111790.00 T
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Описание: Transfer functions and characteristic functions proved to be key in operator theory and system theory. Moshe Livic played a major role in developing these functions, and this book of papers dedicated to his memory covers a wide variety of topics in the field.

Автор: A. Kuzhel
Название: Characteristic Functions and Models of Nonself-Adjoint Operators
ISBN: 9401065667 ISBN-13(EAN): 9789401065665
Издательство: Springer
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Цена: 88500.00 T
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Описание: Over the last decades, the study of nonself-adjoint or nonunitary operators has been mainly based on the method of characteristic functions and on methods of model construction or dilatation for corresponding operator classes.

Автор: Damir Z. Arov; Harry Dym
Название: Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems
ISBN: 303009944X ISBN-13(EAN): 9783030099442
Издательство: Springer
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Цена: 102480.00 T
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Описание: 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.