UID:
almahu_9949450752002882
Format:
XII, 262 p. 1 illus. in color.
,
online resource.
Edition:
1st ed. 2022.
ISBN:
9783031052965
Series Statement:
Lecture Notes in Mathematics, 2315
Content:
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.
In:
Springer Nature eBook
Additional Edition:
Printed edition: ISBN 9783031052958
Additional Edition:
Printed edition: ISBN 9783031052972
Language:
English
DOI:
10.1007/978-3-031-05296-5
URL:
https://doi.org/10.1007/978-3-031-05296-5
