A Guide to Generalized Functions

Linear, Nonlinear, Random, and Infinite Dimensional Distributions

Uluğ Çapar (Autor)

Buch | Hardcover

XVIII, 348 Seiten

2026
Springer International Publishing (Verlag)
978-3-032-09183-3 (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.

Ulug Çapar is an emeritus professor of mathematics from Sabanci University in Istanbul, Turkey. His first degree was in engineering with continuum mechanics as option. Two professors influenced him to reshape his professional career as a mathematician. The first one was the most celebrated Turkish mathematician Cahit Arf. The second one was Jan Mikusinski, a leading figure of the theory of generalized functions (distributions). The subject has become part of the author s lifetime academic occupation except that his interests have shifted in the long run to its nonlinear and random versions. He was a student in graduate courses offered by both of them. Prof. Arf would also become his colleague in his last years at the Middle East Technical University (M.E.T.U.), Ankara.

Chapter 1. Linear Distributions.- Chapter 2. Some Applications of Linear Distributions.- Chapter 3. Non-linear Distributions.- Chapter 4. Random Distributions.- Chapter 5. Infinite Dimensional Distributions.

Erscheinungsdatum	29.11.2025
Zusatzinfo	XVIII, 348 p. 15 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	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	3-032-09183-7 / 3032091837
ISBN-13	978-3-032-09183-3 / 9783032091833
Zustand	Neuware