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Selected Papers of Takeyuki Hida

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Product Details

  • ISBN-13: 9789810243333
  • Publisher: World Scientific Publishing Company, Incorporated
  • Publication date: 4/2/2001
  • Pages: 496
  • Product dimensions: 6.92 (w) x 10.12 (h) x 1.38 (d)

Table of Contents

Preface
I General Theory of White Noise Functionals
1 Analysis of Brownian Functionals 1
2 Quadratic Functionals of Brownian Motion 47
3 Generalized Brownian Functionals 59
4 The Role of Exponential Functions in the Analysis of Generalized Brownian Functionals 62
5 Causal Calculus and An Application to Prediction Theory 67
6 Generalized Gaussian Measures 75
7 The Impact of Classical Functional Analysis on White Noise Calculus 83
II Gaussian and Other Processes
8 Canonical Representations of Gaussian Processes and Their Applications 95
9 Analysis of Hilbert Space with Reproducing Kernel Arising from Multiple Wiener Integral 142
10 The Square of a Gaussian Markov Process and Nonlinear Prediction 169
III Infinite Dimensional Harmonic Analysis and Rotation Group
11 Sur l'invariance Projective pour les Processus Symetriques Stables 180
12 Note on the Infinite Dimensional Laplacian Operator 183
13 L'analyse Harmonique sur l'espace des Fonctions Generalisees 190
14 Conformal Invariance of White Noise 193
15 Transformations for White Noise Functionals 205
16 On Projective Invariance of Brownian Motion 224
17 Infinite Dimensional Rotations and Laplacians in Terms of White Noise Calculus 239
18 Infinite Dimensional Rotation Group and White Noise Analysis 268
IV Quantum Theory
19 On Quantum Theory in Terms of White Noise 277
20 White noise Analysis and Its Applications to Quantum Dynamics 291
21 Boson Fock Representations of Stochastic Processes 305
V Feynman Integrals and Random Fields
22 Generalized Brownian Functionals and the Feynman Integral 316
23 Dirichlet Forms and White Noise Analysis 331
24 Dirichlet Forms in Terms of White Noise Analysis I: Construction and QFT Examples 342
25 Dirichlet Forms in Terms of White Noise Analysis II: Closability and Diffusion Processes 364
VI Variational Calculus and Random Fields
26 Multidimensional Parameter White Noise and Gaussian Random Fields 375
27 A Note on Generalized Gaussian Random Fields 382
28 White Noise and Stochastic Variational Calculus for Gaussian Random Fields 388
29 Variational Calculus for Gaussian Random Fields 400
30 Innovations for Random Fields 409
VII Application to Biology
31 Functional Word in a Protein I. Overlapping Words 420
Comments on [11], [14], [19], [20] and [21] 427
Comments on [6], [8], [10], [27] and [29] 434
Comments on [9], [11], [14], [16], [17] and [18] 437
Comments on [1], [2], [4] and [5] 439
Comments on [12], [13], [16] and [17] 442
Comments on [15] and [31] 445
Comments on [26], [28] and [30] 446
Comments on [20], [22], [23], [24] and [25] 448
My Mathematical Journey 453
List of Publications 475
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