A Guide to Generalized Functions

Beschreibung

The aim of the present work is to give a unifying treatment of the four faces of the theory of generalized functions – linear, nonlinear, random and infinite dimensional distributions. The book deals with all of these categories in a comparative and interconnected way, giving a broad overview without getting lost in too many details.   This original presentation touches upon a number of mathematical areas, such as functional analysis, theory of functions, measure theory, operator theory, differentiable manifolds, probability theory, stochastic processes and stochastic analysis. For example, in one of the chapters it builds a bridge from Gaussian measures on Hilbert spaces, Malliavin calculus, Wiener chaos, Meyer-Watanabe distributions, Hida distributions and White Noise Analysis up to Kondratiev spaces, ending with Colombeau versions.   Any researcher who is looking for an overview on the state-of-the art, or to specialize in the theory of distributions, will find this book a useful resource.
The aim of the present work is to give a unifying treatment of the four faces of the theory of generalized functions – linear, nonlinear, random and infinite dimensional distributions. The book deals with all of these categories in a comparative and interconnected way, giving a broad overview without getting lost in too many details.   This original presentation touches upon a number of mathematical areas, such as functional analysis, theory of functions, measure theory, operator theory, differentiable manifolds, probability theory, stochastic processes and stochastic analysis. For example, in one of the chapters it builds a bridge from Gaussian measures on Hilbert spaces, Malliavin calculus, Wiener chaos, Meyer-Watanabe distributions, Hida distributions and White Noise Analysis up to Kondratiev spaces, ending with Colombeau versions.   Any researcher who is looking for an overview on the state-of-the art, or to specialize in the theory of distributions, will find this book a useful resource.
Very few publications on random distributions Provides a fast entrance into the theory of generalized functions Includes the interconnections of four types of distributions Shows distributions can be incorporated into your research work

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Uluğ Çapar

Themen in »A Guide to Generalized Functions«

Tempered distributions Ornstein-Uhlenbeck semigroup Distributions of compact support Gross theorem Schwartz functions Nuclear operators Fock spaces Schwartz distributions Meyer-Watanabe distributions Tensor product of Hilbert spaces and Gaussian probability spaces Cylinder measures and cylinder probabilities Second quantization operator Hida distributions Compact operators Frechet spaces

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