Exclusive web offer for individuals on print books. Terms & Conditions may apply.
Sale ends 22nd September 2019.
Chapman and Hall/CRC
182 pages
The first book to examine weakly stationary random fields and their connections with invariant subspaces (an area associated with functional analysis). It reviews current literature, presents central issues and most important results within the area. For advanced Ph.D. students, researchers, especially those conducting research on Gaussian theory.
Introduction
Weakly Stationary Sequences
Preliminaries
Examples of Weakly Stationary Sequences
Spectral Representation of the Covariance Function
Examples of Spectral Measures
Canonical Isomorphism between L2(T; FX) and L(X)
Spectral Representation of a Weakly Stationary Sequence
The Shift Operator on L(X)
Moving Averages and Densities
Regular and Singular Sequences
Examples of Regular and Singular Sequences
The Wold Decomposition
The Theory of Regular Sequences
The Concordance Theorem
Maximal Factors and Innovation Processes
The Szego-Krein-Kolmogorov Theorem
Weakly Stationary Random Fields
Preliminaries
Examples
Random Field with Discrete Spectral Measure
Product Random Field
White Noise Random Field
Moving Average Random Field
Regularity and Singularity
Examples
Horizontally and Vertically Singular
Horizontally Regular and Vertically Singular
Horizontally and Vertically Regular
Horizontal and Vertical Wold Decomposition
Regularity and the Spectral Measure
Spectral Measures and Spectral-type Wold Decompositions
The Fourfold Wold Decomposition
Quarter-plane Moving Average Representations
Helson-Lowdenslager Theory
Semi-group Moving Average Representations
Wold-Type Decompositions
Invariant Subspaces
The Halmos Decomposition
Invariant Subspaces of L2(T)
Invariant Subspaces of H2(T)
The Halmos Fourfold Decomposition
The Doubly Commuting Condition
Invariant Subspaces of L2(T2)
Invariant Subspaces of H2(T2)
Applications and Generalizations
Texture Identi_cation
Invariant Subspaces of Lp(T)
Harmonizable S_S Sequences
Invariant Subspaces of Lp(T2)
Harmonizable S_S Fields
Proper MA Representations and Outer Functions
Background Material
Projections
Orthogonally Scattered Set Functions
Representation Theorems
Bibliography
