Selected Papers of Takeyuki Hida

Selected Papers of Takeyuki Hida

by Takeyuki Hida

ISBN-10: 9810243332

ISBN-13: 9789810243333

Pub. Date: 04/02/2001

Publisher: World Scientific Publishing Company, Incorporated

Product Details

World Scientific Publishing Company, Incorporated
Publication date:
Product dimensions:
6.92(w) x 10.12(h) x 1.38(d)

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Table of Contents

IGeneral Theory of White Noise Functionals
1Analysis of Brownian Functionals1
2Quadratic Functionals of Brownian Motion47
3Generalized Brownian Functionals59
4The Role of Exponential Functions in the Analysis of Generalized Brownian Functionals62
5Causal Calculus and An Application to Prediction Theory67
6Generalized Gaussian Measures75
7The Impact of Classical Functional Analysis on White Noise Calculus83
IIGaussian and Other Processes
8Canonical Representations of Gaussian Processes and Their Applications95
9Analysis of Hilbert Space with Reproducing Kernel Arising from Multiple Wiener Integral142
10The Square of a Gaussian Markov Process and Nonlinear Prediction169
IIIInfinite Dimensional Harmonic Analysis and Rotation Group
11Sur l'invariance Projective pour les Processus Symetriques Stables180
12Note on the Infinite Dimensional Laplacian Operator183
13L'analyse Harmonique sur l'espace des Fonctions Generalisees190
14Conformal Invariance of White Noise193
15Transformations for White Noise Functionals205
16On Projective Invariance of Brownian Motion224
17Infinite Dimensional Rotations and Laplacians in Terms of White Noise Calculus239
18Infinite Dimensional Rotation Group and White Noise Analysis268
IVQuantum Theory
19On Quantum Theory in Terms of White Noise277
20White noise Analysis and Its Applications to Quantum Dynamics291
21Boson Fock Representations of Stochastic Processes305
VFeynman Integrals and Random Fields
22Generalized Brownian Functionals and the Feynman Integral316
23Dirichlet Forms and White Noise Analysis331
24Dirichlet Forms in Terms of White Noise Analysis I: Construction and QFT Examples342
25Dirichlet Forms in Terms of White Noise Analysis II: Closability and Diffusion Processes364
VIVariational Calculus and Random Fields
26Multidimensional Parameter White Noise and Gaussian Random Fields375
27A Note on Generalized Gaussian Random Fields382
28White Noise and Stochastic Variational Calculus for Gaussian Random Fields388
29Variational Calculus for Gaussian Random Fields400
30Innovations for Random Fields409
VIIApplication to Biology
31Functional Word in a Protein I. Overlapping Words420
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 Journey453
List of Publications475

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