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This monograph presents a framework for infinite dimensional analysis based on white noise. This approach, which has many areas of application is both intuitive and efficient.
Among the concepts and structures generalized to an infinite dimensional setting in this book are: spaces of test and generalized functions, differential calculus, Laplacian and Fourier transforms and Dirichlet forms and their Markov processes. A multitude of concepts, such as Brownian motion functionals, falls into this framework. This book presents a simple, yet general theory of shastic integration and also discusses construction quantum field theory and Feynman's functional integration.
This volume will be of interest to mathematicians and scientists who use shastic methods in their research. The book will be of particular value to mathematicians in probability theory, functional analysis, measure theory, potential theory, as well as to physicists and scientists in engineering.
Preface. Notations and Convention. 1. Gaussian Spaces. 2. T and S Transformation and the Decomposition Theorem. 3. Generalized Functionals. 4. The Spaces (S) and (S)*. 5. Calculus of Differential Operators. 6. Laplacian Operators. 7. The Spaces D and D*. 8. Shastic Integration. 9. Fourier and Fourier-Mehler Transforms. 10. Dirichlet Forms. 11. Applications to Quantum Field Theory. 12. Feynman Integrals. Appendices. Bibliography.
Posted October 20, 2011
The bood is authored by T. Hida, a great scholar in his field, and others. The book contains many chapters for almost all materials needed to understand the topics. So it can be used as a textbook for graduate students, as well as a valuable reference book to mathematicians and physicists in stochastic analysis and quantum field theory. It is also useful for engineers and economists who need stochastic calculus. However, the printing is not the best--not using LaTex format for lots of symbols makes them hard to be recognized and even look a little ugly, although considering the year it was published (1993), this was understandable. Hope the printing will be improved in its 2nd edition.Was this review helpful? Yes NoThank you for your feedback. Report this reviewThank you, this review has been flagged.