Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems: 266 (Operator Theory: Advances and Applications) - Tapa blanda
Libro 113 de 132: Operator Theory: Advances and Applications
Sinopsis
Introduction.- Analytic preliminaries.- The de Branges spaces B(E) and H(A).- Three extension problems.- Spectral functions for ci problems.- Inverse spectral problems.- Generalizations.- Real and symmetric constraints.- Past and Future.- Conservative and passive systems.- Rational spectral densities.
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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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Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems (Operator Theory: Advances and Applications, 266)
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Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems
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Taschenbuch. Condición: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 420 pp. Englisch. Nº de ref. del artículo: 9783030099442
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Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems
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Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems
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Condición: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt.    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 count. Nº de ref. del artículo: 448672575
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Taschenbuch. Condición: Neu. Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems | Harry Dym (u. a.) | Taschenbuch | xiv | Englisch | 2018 | Springer | EAN 9783030099442 | Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. Nº de ref. del artículo: 116683895
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Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems
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Taschenbuch. Condición: Neu. This item is printed on demand - Print on Demand Titel. Neuware Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 420 pp. Englisch. Nº de ref. del artículo: 9783030099442
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Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems
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Taschenbuch. Condición: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Nº de ref. del artículo: 9783030099442
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