Spectral Methods in Infinite-Dimensional Analysis

ISBN-13: 9780792328490 / Angielski / Twarda / 1995 / 1010 str.

Iu M. Berezanskii; Y. M. Berezansky; Y. G. Kondratiev

Opis

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.

Spis treści

Contents Volume I: Preface to the English Edition. Preface. Introduction. 1. Rigged Spaces. 2. Generalized Functions of Infinitely Many Variables. Gaussian Measures. 3. Spectral Theorem. 4. Representations by Commuting Operators. Bibliographical Notes. References. Subject Index. List of Notations. Contents Volume II: 5. Application of the Theory of Expansions to the Harmonic Analysis. 6. Infinite-Dimensional Elliptic Differential Operators of the Second Order. 7. Infinite-Dimensional Differential Operators in the Models of Quantum Statistical Physics and Field Theory. Bibliographical Notes. References. Subject Index. List of Notations.