عنوان

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

شابک

3319702629

شابک

9783319702629

شابک اشتباه

3319702610

شابک اشتباه

9783319702612

عنوان اصلي

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

نام عام مواد

[Book]

نام نخستين پديدآور

Damir Z. Arov, Harry Dym.

محل نشرو پخش و غیره

Cham, Switzerland :

نام ناشر، پخش کننده و غيره

Birkhäuser,

تاریخ نشرو بخش و غیره

2018.

نام خاص و کميت اثر

1 online resource

عنوان فروست

Operator theory: advances and applications ;

مشخصه جلد

volume 266

متن يادداشت

Includes bibliographical references and index.

متن يادداشت

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.

متن يادداشت

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

بدون عنوان

0

بدون عنوان

8

متن يادداشت

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.

عنوان

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

شماره استاندارد بين المللي کتاب و موسيقي

9783319702612

موضوع مستند نشده

Multivariate analysis.

موضوع مستند نشده

Prediction theory.

موضوع مستند نشده

Mathematics

موضوع مستند نشده

Operator Theory

موضوع مستند نشده

Probability Theory and Stochastic Processes

موضوع مستند نشده

MATHEMATICS-- Applied.

موضوع مستند نشده

MATHEMATICS-- Probability & Statistics-- General.

موضوع مستند نشده

Multivariate analysis.

موضوع مستند نشده

Prediction theory.

موضوع مستند نشده

MAT-- 003000

موضوع مستند نشده

MAT-- 029000

شماره

ويراست

شماره رده

مستند نام اشخاص تاييد نشده

Arov, Damir Z.

مستند نام اشخاص تاييد نشده

Dym, H., (Harry),1938-

تاريخ عمليات

20200823102909.0

قواعد فهرست نويسي ( بخش توصيفي )

pn

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y