Kimiaki Saito - Böcker

This text is dedicated to Professor Takeyuki Hida on the occasion of his 70th birthday. The book is more than a collection of articles, it is a consistent editorial work, devoted to attempting to obtain a unitary picture from the different contributions and to give a comprehensive account of important developments in contemporary white noise analysis and some of its applications. For this reason, not only the results, but also motivations, explanations and connections with previous work have been included. The wealth of applications, from number theory to signal processing, from optimal filtering to information theory, from the statistics of stationary flows to quantum cable equations, show the power of white noise analysis as a tool. Beyond these, the authors emphasize its connections with practically all branches of contemporary probability, including stochastic geometry, the structure theory of stationary Gaussian processes, Neumann boundary value problems, and large deviations.

Recent Developments in Infinite-Dimensional Analysis and Quantum Probability is dedicated to Professor Takeyuki Hida on the occasion of his 70th birthday. The book is more than a collection of articles. In fact, in it the reader will find a consistent editorial work, devoted to attempting to obtain a unitary picture from the different contributions and to give a comprehensive account of important recent developments in contemporary white noise analysis and some of its applications. For this reason, not only the latest results, but also motivations, explanations and connections with previous work have been included. The wealth of applications, from number theory to signal processing, from optimal filtering to information theory, from the statistics of stationary flows to quantum cable equations, show the power of white noise analysis as a tool. Beyond these, the authors emphasize its connections with practically all branches of contemporary probability, including stochastic geometry, the structure theory of stationary Gaussian processes, Neumann boundary value problems, and large deviations.

The topics covered in this proceedings include the C* — dynamical systems, the index theory of subfactors, the noncommutative differential geometry and the quantum groups. This volume presents an overview of the present status of the theory of operator algebras, as well as an outlook for its future development.

Elementary presentations of different topics in the theory of singularities, together with the most recent results in this field are included in these proceedings. The book is aimed at graduate students who are interested to learn about singularities and scientists with a mathematical background who need a better understanding of the field.

The topics discussed in this book can be classified into three parts:(i) Gaussian processes. The most general and in fact final representation theory of Gaussian processes is included in this book. This theory is still referred to often and its developments are discussed.(ii) White noise analysis. This book includes the notes of the series of lectures delivered in 1975 at Carleton University in Ottawa. They describe the very original idea of introducing the notion of generalized Brownian functionals (nowadays called “generalized white noise functionals”, and sometimes “Hida distribution”.(iii) Variational calculus for random fields. This topic will certainly represent one of the driving research lines for probability theory in the next century, as can be seen from several papers in this volume.

Over the last decade the theory of quantum information has developed into an important and active research area in mathematics, physics and other fields of science. It has established a link among those fields.This volume covers the following topics: Quantum Computation, NP-Complete Problem, Quantum Communication, Quantum Stochastic Processes, Quantum Field Theory, Classical and Quantum White Noise Analysis, Infinite Dimensional Stochastic Analysis, Gaussian Random Fields, Probabilistic Control in Microorganisms, Complexity in Nature, etc.

This volume constitutes the proceedings of the Fourth International Conference on Quantum Information, held in Japan in 2001. Topics covered include: infinite dimensional harmonic analysis; white noise theory; complex Gaussian random fields; quantum information in space and time; and more.

This volume includes the proceedings of the Fifth Conference on Quantum Information held at Meijo University, Japan.

Quantum information is a developing multi-disciplinary field, with many exciting links to white noise theory. This connection is explored and presented in this work, which effectively bridges the gap between quantum information theory and complex systems. Arising from the Meijo Winter School and International Conference, the lecture notes and research papers published in this timely volume will have a significant impact on the future development of the theories of quantum information and complexity. This book will be of interest to mathematicians, physicists, computer scientists as well as electrical engineers working in this field.