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Authors' Note | p. ix |
Preface | p. xi |
Introduction | p. 1 |
Background: Function Theory | |
Harmonic Functions | p. 10 |
Positive Harmonic Functions on the Upper Half-Plane | p. 13 |
Analytic Functions of Exponential Type | p. 16 |
Phragmen-Lindelof Principle | p. 17 |
Poisson-Jensen Formula | p. 18 |
Quotients of Exponential Type | p. 20 |
Carlson's Theorem | p. 21 |
Hadamard Products | p. 21 |
Nevanlinna's Formula | p. 22 |
Background: Hardy Functions | |
Fourier Integrals | p. 26 |
Paley-Wiener Theorem | p. 28 |
Hardy Functions of Class H[superscript 2] | p. 30 |
Projection | p. 33 |
A Basis | p. 34 |
An Inequality | p. 35 |
Inner and Outer Functions | p. 36 |
Tests for Outer Functions | p. 39 |
Hardy Functions of Class H[superscript 1] | p. 42 |
Hardy Functions of Class H[superscript infinity] | p. 46 |
Hilbert Transforms and Conjugate Functions | p. 48 |
Phases | p. 52 |
Inner Functions Again | p. 53 |
Quasi-Analytic Classes | p. 55 |
Background: Probability | |
Gaussian Families | p. 61 |
Independence and Perpendicularity | p. 63 |
Angles | p. 65 |
Degree of Independence | p. 67 |
Mutual Information | p. 68 |
Kolmogorov's Modulus | p. 69 |
Stationary Gaussian Processes | p. 71 |
Spectral Functions | p. 74 |
Metric Transitivity | p. 76 |
Ivankov's Alternative | p. 78 |
Past and Future | |
Kolmogorov-Wiener Prediction Problem | p. 82 |
Szego's Alternative | p. 83 |
Doing the Prediction | p. 87 |
Wiener's Formula | p. 90 |
Filters and White Noise | p. 92 |
Past and Future | p. 96 |
Rational Spectral Densities | p. 100 |
Type Spaces | p. 108 |
Splitting | p. 117 |
Germ and Gap | p. 121 |
Okabe's Formulas | p. 126 |
Mixing | p. 130 |
Interpolation | p. 136 |
Strings and Spectral Functions | |
Strings | p. 147 |
Self-Adjoint Operators | p. 153 |
Feller's Theorem | p. 159 |
Green Functions | p. 162 |
Principal Spectral Functions | p. 176 |
Traces | p. 181 |
Transforms | p. 185 |
The Backwards Problem | p. 194 |
Stieltjes' Investigations | p. 203 |
Nonprincipal Spectral Functions | p. 208 |
Strings and Spaces of Integral Functions | |
De Branges Spaces | p. 221 |
Short de Branges Spaces | p. 228 |
Short Spaces and Short Strings | p. 233 |
Type Spaces | p. 241 |
Nesting of Short Spaces | p. 247 |
Recovering the String | p. 252 |
Hardy Densities | p. 255 |
Dual Strings | p. 262 |
Change of Scale and Mass | p. 264 |
Prediction Using Part of the Past | p. 279 |
Short Processes | p. 291 |
A New Class of Strings | p. 293 |
Strings for Interpolation | p. 306 |
Interpolation: Examples | p. 318 |
References | p. 323 |
Index | p. 329 |
Table of Contents provided by Ingram. All Rights Reserved. |
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The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.