Many areas of applied mathematics call for an efficient calculus in infinite dimensions. This is most apparent in quantum physics and in all disciplines of science which describe natural phenomena by equations involving stochasticity. With this monograph we intend to provide a framework for analysis in infinite dimensions which is flexible enough to be applicable in many areas, and which on the other hand is intuitive and efficient. Whether or not we achieved our aim must be left to the judgment of the reader. This book treats the theory and applications of analysis and functional analysis in...

The first paper in this volume, by T. Ray, aims to create an instantiation of evolution by natural selection in the computational medium. The second, by K. Naka, discusses the application of white noise analysis to the retinal physiology. It deals with indentification of the retina mathematically, and the reader is shown the results that can be discovered only by using white noise analysis. The last paper, by T. Hilda, illustrates the use of white noise analysis for biologists. It presents the types of topics to which white noise anaysis can be applied and how to apply the theory to actual...

This volume constitutes the proceedings of the Second International Conference on Quantum Information, held at Meijo University, Japan, in 1999. Topics addressed include: CKS-space in terms of growth functions; Gaussian processes and Gaussian random fields; and more.

Over the last decade the theory of quantum information has developed into an important an active research area in mathematics, physics an 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 Field Probabilistic Control in Microorganisms Complexity in Nature, etc.

During the last fifty years, Gopinath Kallianpur has made extensive and significant contributions to diverse areas of probability and statistics, including stochastic finance, Fisher consistent estimation, non-linear prediction and filtering problems, zero-one laws for Gaussian processes and reproducing kernel Hilbert space theory, and stochastic differential equations in infinite dimensions. To honor Kallianpur's pioneering work and scholarly achievements, a number of leading experts have written research articles highlighting progress and new directions of research in these and related...

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...

Following the publication of the Japanese edition of this book, several inter- esting developments took place in the area. The author wanted to describe some of these, as well as to offer suggestions concerning future problems which he hoped would stimulate readers working in this field. For these reasons, Chapter 8 was added. Apart from the additional chapter and a few minor changes made by the author, this translation closely follows the text of the original Japanese edition. We would like to thank Professor J. L. Doob for his helpful comments on the English edition. T. Hida T. P. Speed v...