| Preface |
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vii | |
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1 Harmonizability And Stochastic Analysis |
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1 | (42) |
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1.1 Second Order Processes and Stationarity |
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1 | (2) |
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1.2 Admissible Means for Stationary Processes and Extensions |
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3 | (14) |
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1.3 Positive Definiteness as a Basis of Stochastic Analysis |
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17 | (15) |
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1.4 Important Remarks on Abstract and Concrete Versions of Hilbert Spaces |
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32 | (4) |
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1.5 Complements and Exercises |
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36 | (3) |
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1.6 Bibliographical Notes |
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39 | (4) |
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2 Harmonic Approaches For Integrable Processes |
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43 | (88) |
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2.1 Morse-Transue Integration Method and Stochastic Analysis |
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43 | (16) |
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2.2 V-Boundedness, Weak and Strong Harmonizabilities |
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59 | (13) |
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2.3 Harmonizability and Stationary Dilations for Applications |
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72 | (5) |
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2.4 Domination of Vector Measures and Application to Cramer and Karhunen Processes |
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77 | (10) |
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2.5 Multiple Generalized Random Fields |
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87 | (15) |
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2.6 Local Functionals in Probability; Their Integral Representations and Applications |
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102 | (7) |
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2.7 A Probabilistic Proof of Riemann's Hypothesis |
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109 | (6) |
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2.8 Admissible Means of Second Order Processes |
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115 | (7) |
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2.9 Complements and Exercises |
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122 | (5) |
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2.10 Bibliographical Notes |
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127 | (4) |
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3 Applications And Extensions Of Harmonizable Processes |
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131 | (46) |
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3.1 Special Classes of Weak Harmonizability |
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131 | (10) |
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3.2 Linear Models for Weakly Harmonizable Classes |
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141 | (5) |
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3.3 Application to Signal Extraction from Noise, and Sampling |
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146 | (11) |
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3.4 Class (KF) and Nonstationary Processes Applications |
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157 | (7) |
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3.5 Further Classifications and Representations of Second Order Processes |
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164 | (7) |
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3.6 Complements and Exercises |
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171 | (4) |
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3.7 Bibliographical Notes |
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175 | (2) |
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4 Isotropic Harmonizable Fields And Applications |
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177 | (52) |
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4.1 Harmonizability for Multiple Indexed Random Classes |
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177 | (8) |
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4.2 A Classification of Isotropic Covariances |
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185 | (10) |
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4.3 Representations of Multiple Generalized Random Fields |
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195 | (6) |
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4.4 Remarks on Harmonizability and Isotropy for Generalized Fields |
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201 | (2) |
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4.5 Summability Methods for Second Order Random Processes |
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203 | (3) |
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4.6 Prediction Problems for Stochastic Flows |
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206 | (17) |
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4.7 Complements and Exercises |
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223 | (4) |
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4.8 Bibliographical Notes |
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227 | (2) |
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5 Harmonizable Fields On Groups And Hypergroups |
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229 | (30) |
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5.1 Bimeasures and Morse-Transue (or MT-) Integrals |
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229 | (5) |
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5.2 Harmonizability on LCA Groups |
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234 | (11) |
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5.3 Harmonizability on Hypergroups |
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245 | (2) |
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5.4 Remarks on Strict Harmonizability and V-Boundedness |
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247 | (2) |
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5.5 Vector-Valued Harmonizable Random Fields |
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249 | (1) |
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5.6 Cramer and Karhunen Extensions of Harmonizability Compared |
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250 | (1) |
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5.7 Complements and Exercises |
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251 | (5) |
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5.8 Bibliographical Notes |
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256 | (3) |
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6 Some Extensions Of Harmonizable Random Fields |
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259 | (44) |
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259 | (1) |
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6.2 Harmonizability, Isotropy and Their Analyses |
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260 | (9) |
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6.3 Some Moving Averages and Sampling of Harmonizable Classes |
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269 | (13) |
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6.4 Multivariate Harmonizable Random Fields |
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282 | (7) |
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6.5 Optimum Harmonizable Filtering with Squared Loss |
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289 | (5) |
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6.6 Applications and Extensions of Harmonizable Fields |
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294 | (3) |
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6.7 Complements and Exercises |
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297 | (4) |
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6.8 Bibliographical Notes |
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301 | (2) |
| Bibliography |
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303 | (18) |
| Notation Index |
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321 | (2) |
| Author Index |
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323 | (4) |
| Subject Index |
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327 | |
