Weakly Stationary Random Fields Invariant Subspaces and Applications 1st Edition by Vidyadhar S Mandrekar, David A Redett ISBN 1138562246 9781138562240

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ISBN 10: 1138562246 
ISBN 13: 9781138562240
Author: Vidyadhar S Mandrekar, David A Redett

Weakly Stationary Random Fields Invariant Subspaces and Applications 1st Table of contents:

1. Weakly Stationary Sequences
1.1 Preliminaries
1.2 Examples of Weakly Stationary Sequences
1.3 Spectral Representation of the Covariance Function
1.4 Examples of Spectral Measures
1.5 Canonical Isomorphism between and L(X)
1.6 Spectral Representation of a Weakly Stationary Sequence
1.7 The Shift Operator on L(X)
1.8 Moving Averages and Densities
1.9 Regular and Singular Sequences
1.10 Examples of Regular and Singular Sequences
1.11 The Wold Decomposition
1.12 The Theory of Regular Sequences
1.13 The Concordance Theorem
1.14 Maximal Factors and Innovation Processes
1.15 The Szegö-Krein-Kolmogorov Theorem
1.16 Remarks and Related Literature
2. Weakly Stationary Random Fields
2.1 Preliminaries
2.2 Examples
2.2.1 Random Field with Discrete Spectral Measure
2.2.2 Product Random Field
2.2.3 White Noise Random Field
2.2.4 Moving Average Random Field
2.3 Regularity and Singularity
2.4 Examples
2.4.1 Horizontally and Vertically Singular
2.4.2 Horizontally Regular and Vertically Singular
2.4.3 Horizontally and Vertically Regular
2.5 Horizontal and Vertical Wold Decomposition
2.6 Regularity and the Spectral Measure
2.7 Spectral Measures and Spectral-type Wold Decompositions
2.8 The Fourfold Wold Decomposition
2.9 Quarter-plane Moving Average Representations
2.10 Helson-Lowdenslager Theory
2.11 Semigroup Moving Average Representations
2.12 Wold-Type Decompositions
2.13 Remarks and Related Literature
3. Invariant Subspaces
3.1 The Halmos Decomposition
3.2 Invariant Subspaces of
3.3 Invariant Subspaces of
3.4 The Halmos Fourfold Decomposition
3.5 The Doubly Commuting Condition
3.6 Invariant Subspaces of
3.7 Invariant Subspaces of
3.8 Remarks and Related Literature
4. Applications and Generalizations
4.1 Texture Identification
4.2 Invariant Subspaces of
4.3 Harmonizable Sequences
4.4 Invariant Subspaces of
4.5 Harmonizable Fields
4.6 Proper MA Representations and Outer Functions
4.7 Remarks and Related Literature
A: Background Material
A.1 Projections
A.2 Orthogonally Scattered Set Functions
A.3 Representation Theorems

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Tags: Vidyadhar S Mandrekar, David A Redett, Weakly Stationary, Fields Invariant