(Pure and Applied Mathematics_ A Wiley Series of Texts, Monographs and Tracts ) Ioannis Antoniou, Baidyanath Misra, Zdzislaw Suchanecki-Time Operator, Innovation and Complexity (Draft)-John Wiley & So.pdf

文档介绍：Time Operator
Time Operator
Innovation plexity
I. Antoniou
B. Misra
Z. Suchanecki
A Wiley-Interscience Publication
JOHN WILEY & SONS, INC.
New York / Chichester / Weinheim / Brisbane / Singapore / Toronto
Contents
Preface ix
Acknowledgments xi
Introduction xiii
1 Predictability and innovation 1
Dynamical systems 2
Dynamical systems associated with maps 4
The ergodic hierarchy 6
Evolution operators 9
Ergodic properties of dynamical systems – operator
approach 12
Innovation and time operator 14
2 Time operator of Kolmogorov systems 21
3 Time operator of the baker map 29
4 Time operator of relativistic systems 33
5 Time operator of exact systems 35
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vi CONTENTS
Exact systems 35
Time operator of unilateral shift 38
Time operator of bilateral shift 44
6 Time operator of the Renyi map and the Haar wavelets 47
Non-uniform time operator of the Renyi map 48
The domain of the time operator 52
The Haar wavelets on the interval 54
Relations between the time operators of the Renyi and
baker maps 56
The uniform time operator for the Renyi map 58
7 Time operator of the cusp map 61
8 Time operator of stationary stochastic processes 65
Time operator of the stochastic processes stationary
in wide sense 68
Time operators of strictly stationary processes - Fock
space 73
9 Time operator of diffusion processes 77
Time Operators for Semigroups and Intertwining 78
Intertwining of the Diffusion Equation with the
Unilateral Shift 79
The Time Operator of the Diffusion Semigroup 82
The Spectral Resolution of the Time Operator 85
Age Eigenfunctions and Shift Representation of the
Solution of the Diffusion Equation 86
Time Operator of the Telegraphist Equation 87
Nonlocal Entropy Operator for the Diffusion Equation 88
10 Time operator of self-similar processes 91
11 Time operator of Markov processes 97
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