Convolution-like Structures, Differential Operators and Diffusion Processes

Rúben Sousa, Manuel Guerra, Semyon B. Yakubovich

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English

Springer International Publishing AG
28 July 2022

Functional analysis & transforms; Integral calculus & equations; Probability & statistics

Series: Lecture Notes in Mathematics

Summary
Details

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 Xt 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 Xt 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.

By: Rúben Sousa, Manuel Guerra, Semyon B. Yakubovich
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 1st ed. 2022
Volume: 2315
Dimensions: Height: 235mm, Width: 155mm,
Weight: 427g
ISBN: 9783031052958
ISBN 10: 3031052951
Series: Lecture Notes in Mathematics
Pages: 262
Publication Date: 28 July 2022
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active