Ebook: Spectral Methods in Infinite-Dimensional Analysis
- Tags: Functional Analysis, Operator Theory, Measure and Integration, Elementary Particles Quantum Field Theory, Statistical Physics Dynamical Systems and Complexity
- Series: Mathematical Physics and Applied Mathematics 12/1-2
- Year: 1995
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- pdf
The Russian edition of this book appeared 5 years ago. Since that time, many results have been improved upon and new approaches to the problems investigated in the book have appeared. But the greatest surprise for us was to discover that there exists a large group of mathematicians working in the area of the so-called White Noise Analysis which is closely connected with the essential part of our book, namely, with the theory of generalized functions of infinitely many variables. The first papers dealing with White Noise Analysis were written by T. Hida in Japan in 1975. Later, this analysis was devel oped intensively in Japan, Germany, U.S.A., Taipei, and in other places. The related problems of infinite-dimensional analysis have been studied in Kiev since 1967, and the theory of generalized functions of infinitely many variables has been in vestigated since 1973. However, due to the political system in the U.S.S.R., contact be tween Ukrainian and foreign mathematicians was impossible for a long period of time. This is why, to our great regret, only at the end of 1988 did one of the authors meet L. Streit who told him about the existence of White Noise Analysis. And it become clear that many results in these two theories coincide and that, in fact, there exists a single theory and not two distinct ones.
Content:
Front Matter....Pages i-xvii
Rigged Spaces....Pages 1-77
Generalized Functions of Infinitely Many Variables. Gaussian Measures....Pages 79-258
Spectral Theorem....Pages 259-407
Representations by Commuting Operators....Pages 409-521
Application of the Theory of Expansions to Harmonic Analysis....Pages 522-701
Infinite-Dimensional Elliptic Differential operators of the Second Order....Pages 702-819
Infinite-Dimensional Differential Operators in the Models of Quantum Statistical Physics and Field Theory....Pages 820-890
Back Matter....Pages 891-949
Content:
Front Matter....Pages i-xvii
Rigged Spaces....Pages 1-77
Generalized Functions of Infinitely Many Variables. Gaussian Measures....Pages 79-258
Spectral Theorem....Pages 259-407
Representations by Commuting Operators....Pages 409-521
Application of the Theory of Expansions to Harmonic Analysis....Pages 522-701
Infinite-Dimensional Elliptic Differential operators of the Second Order....Pages 702-819
Infinite-Dimensional Differential Operators in the Models of Quantum Statistical Physics and Field Theory....Pages 820-890
Back Matter....Pages 891-949
....