Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems. 1st ed. 2018

種類:

電子ブック

責任表示:

by Damir Z. Arov, Harry Dym

出版情報:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2018

著者名:

• Arov, Damir Z.
• Dym, Harry.
• SpringerLink (Online service)

シリーズ名:

Operator Theory: Advances and Applications ; 266

ISBN:

9783319702629 [3319702629]    

注記:

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 rat

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