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1 066 kr
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This two-volume work is devoted to the methods of the spectral theory of operators and the important role they play in infinite-dimensional analysis and its applications. Central to this study is the theory of the expansion of general eigenfunctions for families of commuting self-adjoint or normal operators. This allows a consideration of commutative models which can be applied to the representation of various commutation relations. Also included is an explanation of the theory of hypercomplex systems with locally compact bases. Applications to harmonic analysis lead to a study of the infinite-dimensional moment problem which is connected to problems of axiomatic field theory, integral representations of positive definite functions and kernels with an infinite number of variables. Infinite-dimensional elliptic differential operators are also studied. Particular consideration is given to second quantization operators and their potential perturbations, as well as Dirichlet operators. Applications to quantum field theory and quantum statistical physics are described in detail.Different variants of the theory of infinite-dimensional distributions are examined and this includes a discussion of an abstract version of white noise analysis. This work should be of interest to research mathematicians and mathematical physicists with an interest in spectral theory and its applications.
1 257 kr
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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.