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

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems/ by Damir Z. Arov, Harry Dym.
作者:	Arov, Damir Z.
其他作者:	Dym, Harry.
面頁冊數:	XIV, 405 p.online resource. :
Contained By:	Springer Nature eBook
標題:	Operator theory. -
電子資源:	https://doi.org/10.1007/978-3-319-70262-9
ISBN:	9783319702629

Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems
Arov, Damir Z.

Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems[electronic resource] /by Damir Z. Arov, Harry Dym. - 1st ed. 2018. - XIV, 405 p.online resource. - Operator Theory: Advances and Applications,2660255-0156 ;. - Operator Theory: Advances and Applications,246.

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. .

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.

ISBN: 9783319702629

Standard No.: 10.1007/978-3-319-70262-9doiSubjects--Topical Terms:

527910
Operator theory.

LC Class. No.: QA329-329.9

Dewey Class. No.: 515.724

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