عنوان

Multivariate prediction, de Branges spaces, and related extension and inverse problems /

(Number (ISBN

3319702629

(Number (ISBN

9783319702629

Erroneous ISBN

3319702610

Erroneous ISBN

9783319702612

Title Proper

Multivariate prediction, de Branges spaces, and related extension and inverse problems /

General Material Designation

[Book]

First Statement of Responsibility

Damir Z. Arov, Harry Dym.

Place of Publication, Distribution, etc.

Cham, Switzerland :

Name of Publisher, Distributor, etc.

Birkhäuser,

Date of Publication, Distribution, etc.

2018.

Specific Material Designation and Extent of Item

1 online resource

Series Title

Operator theory: advances and applications ;

Volume Designation

volume 266

Text of Note

Includes bibliographical references and index.

Text of Note

Intro; Preface; Contents; Chapter 1 Introduction; 1.1 Organization of the monograph; 1.2 Notation; 1.3 de Branges matrices E and de Branges spaces B(E); 1.4 Some basic identifications; 1.5 Direct and inverse spectral problems; 1.6 Jp-inner mvf 's and de Branges matrices; 1.7 Helical extension problems; 1.8 Positive extension problems; 1.9 Accelerant extension problems; 1.10 Inverse spectral problems for Krein systems; 1.11 Prediction for multivariable processes based on a finite segment of the past; Weakly stationary processes; Processes with weakly stationary increments.

Text of Note

2.5 The Stieltjes class2.6 The classes Gp×p∞ (0) and Gp×pa (0); 2.7 The classes Pp×p∞ and Pp×pa; 2.8 The classes ˚ Ap×p∞ and ˚ Ap×p; 2.9 Supplementary notes; Chapter 3 The de Branges Spaces B(E) and H(A); 3.1 Reproducing kernel Hilbert spaces; 3.2 Entire de Branges matrices E and the spaces B(E); 3.3 A characterization of B(E) spaces; 3.4 Connections between E ∈ I(jp) andA ∈ U(Jp); 3.5 The RKHS H(A) and its connection with B(E); 3.6 Closed R0-invariant subspaces of H(A) and B(E); 3.7 Supplementary notes; Chapter 4 Three Extension Problems; 4.1 The helical extension problem

0

8

Text of Note

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.

Title

Multivariate prediction, de Branges spaces, and related extension and inverse problems.

International Standard Book Number

9783319702612

Multivariate analysis.

Prediction theory.

Mathematics

Operator Theory

Probability Theory and Stochastic Processes

MATHEMATICS-- Applied.

MATHEMATICS-- Probability & Statistics-- General.

Multivariate analysis.

Prediction theory.

MAT-- 003000

MAT-- 029000

Number

Edition

Class number

Arov, Damir Z.

Dym, H., (Harry),1938-

Date of Transaction

20200823102909.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y