- 398 pages
- English
- PDF
- Only available on web
About This Book
Generalized Functions, Volume 4: Applications of Harmonic Analysis is devoted to two general topicsādevelopments in the theory of linear topological spaces and construction of harmonic analysis in n-dimensional Euclidean and infinite-dimensional spaces. This volume specifically discusses the bilinear functionals on countably normed spaces, Hilbert-Schmidt operators, and spectral analysis of operators in rigged Hilbert spaces. The general form of positive generalized functions on the space S, continuous positive-definite functions, and conditionally positive generalized functions are also deliberated. This publication likewise considers the mean of a generalized random process, multidimensional generalized random fields, simplest properties of cylinder sets, and definition of Gaussian measures. This book is beneficial to students, specialists, and researchers aiming to acquire knowledge of functional analysis.
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Table of contents
- Front Cover
- Applications of Harmonic Analysis
- Copyright Page
- Table of Contents
- Translator's Note
- Foreword
- CHAPTER I. THE KERNEL THEOREM. NUCLEAR SPACES. RIGGED HILBERT SPACE
- CHAPTER II. Positive and Positive-Definite Generalized Functions
- CHAPTER III. Generalized Random Processes
- CHAPTER IV. MEASURES IN LINEAR TOPOLOGICAL SPACES
- NOTES AND REFERENCES TO THE LITERATURE
- BIBLIOGRAPHY
- SUBJECT INDEX