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Convolution-like structures, differential operators and diffusion processes

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Convolution-like structures, differential operators and diffusion processesby Ruben Sousa, Manuel Guerra, Semyon Yakubovich.
作者:	Sousa, Ruben.
其他作者:	Guerra, Manuel.
出版者:	Cham :Springer International Publishing :2022.
面頁冊數:	xii, 262 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Convolutions (Mathematics)
電子資源:	https://doi.org/10.1007/978-3-031-05296-5
ISBN:	9783031052965$q(electronic bk.)

Convolution-like structures, differential operators and diffusion processes
Sousa, Ruben.

Convolution-like structures, differential operators and diffusion processes[electronic resource] /by Ruben Sousa, Manuel Guerra, Semyon Yakubovich. - Cham :Springer International Publishing :2022. - xii, 262 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 23151617-9692 ;. - Lecture notes in mathematics ;2035..

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.

ISBN: 9783031052965$q(electronic bk.)

Standard No.: 10.1007/978-3-031-05296-5doiSubjects--Topical Terms:

246604
Convolutions (Mathematics)

LC Class. No.: QA601 / .S68 2022

Dewey Class. No.: 515.43

Convolution-like structures, differential operators and diffusion processes
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520 $a 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.
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