A Guide to Generalized Functions - Linear, Nonlinear, Random, and Infinite Dimensional Distributions

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.

List of contents

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.

About the author

Uluğ Çapar is an emeritus professor of mathematics from Sabancı 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.

Product details

• Authors: Ulug Çapar, Uluğ Çapar
• Publisher: Springer, Berlin
• Languages: English, German
• Product format: Hardback
• Release: 06.12.2025
• EAN: 9783032091833
• ISBN: 978-3-0-3209183-3
• Illustrations: Approx. 300 p. 8 illus.
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; Stochastik, Wahrscheinlichkeitsrechnung und Statistik, Functional Analysis, Probability Theory, Frechet Spaces, Schwartz functions, Malliavin Calculus, Meyer's inequality, Gross theorem, Hilbert space operators, Compact operators, White noise spaces, Tempered distributions, Schwartz distributions, Hida distributions, Ornstein-Uhlenbeck semigroup, Nuclear operators, Colombeau algebras, Fock spaces, Cylinder measures and cylinder probabilities, Distributions of compact support, Meyer-Watanabe distributions, Second quantization operator