Convolution-like Structures, Differential Operators and Diffusion Processes

1. Auflage 2022
ISBN: 978-3-031-05295-8
Verlag: Springer International Publishing

Buch, Englisch, Band 2315, 262 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 423 g

Reihe: Lecture Notes in Mathematics

This book provides an introduction to recent developments in the theory of generalized harmonic analysis and its applications. It is well known that convolutions, differential operators and diffusion processes are interconnected: the ordinary convolution commutes with the Laplacian, and the law of Brownian motion has a convolution semigroup property with respect to the ordinary convolution. Seeking to generalize this useful connection, and also motivated by its probabilistic applications, the book focuses on the following question: given a diffusion process X on a metric space E, can we construct a convolution-like operator * on the space of probability measures on E with respect to which the law of X has the *-convolution semigroup property? A detailed analysis highlights the connection between the construction of convolution-like structures and disciplines such as stochastic processes, ordinary and partial differential equations, spectral theory, special functions and integral transforms.The book will be valuable for graduate students and researchers interested in the intersections between harmonic analysis, probability theory and differential equations.

Zielgruppe

Research

Autoren/Hrsg.

Sousa, Rúben

Yakubovich, Semyon

Guerra, Manuel

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

- 1. Introduction. - 2. Preliminaries. - 3. The Whittaker Convolution. - 4. Generalized Convolutions for Sturm-Liouville Operators. - 5. Convolution-Like Structures on Multidimensional Spaces.