A Guide to Generalized Functions
Linear, Nonlinear, Random, and Infinite Dimensional Distributions
Seiten
2026
Springer International Publishing (Hersteller)
978-3-032-09184-0 (ISBN)
Springer International Publishing (Hersteller)
978-3-032-09184-0 (ISBN)
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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.
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.
| Erscheint lt. Verlag | 27.1.2026 |
|---|---|
| Reihe/Serie | Mathematics and Statistics | Mathematics and Statistics (R0) |
| Zusatzinfo | XVIII, 348 p. 15 illus. |
| Verlagsort | Cham |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| Schlagworte | Colombeau algebras • compact operators • Cylinder measures and cylinder probabilities • Distributions of compact support • Fock spaces • Frechet Spaces • Gross theorem • Hida distributions • Hilbert space operators • Malliavin calculus • Meyer's inequality • Meyer-Watanabe distributions • Nuclear operators • Ornstein-Uhlenbeck semigroup • Schwartz distributions • Schwartz functions • Second quantization operator • Tempered distributions • Tensor product of Hilbert spaces and Gaussian probability spaces • White noise spaces |
| ISBN-10 | 3-032-09184-5 / 3032091845 |
| ISBN-13 | 978-3-032-09184-0 / 9783032091840 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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