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Convolution-like structures, differe...

Sousa, Ruben.

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Convolution-like structures, differential operators and diffusion processes

Record Type:	Electronic resources : Monograph/item
Title/Author:	Convolution-like structures, differential operators and diffusion processes/ by Ruben Sousa, Manuel Guerra, Semyon Yakubovich.
Author:	Sousa, Ruben.
other author:	Guerra, Manuel.
Published:	Cham :Springer International Publishing : : 2022.,
Description:	xii, 262 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Convolutions (Mathematics) -
Online resource:	https://doi.org/10.1007/978-3-031-05296-5
ISBN:	9783031052965

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 ;v. 2315..

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

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

646444
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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245 1 0 $a Convolution-like structures, differential operators and diffusion processes $h [electronic resource] / $c by Ruben Sousa, Manuel Guerra, Semyon Yakubovich.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2022.
300 $a xii, 262 p. : $b ill., digital ; $c 24 cm.
490 1 $a Lecture notes in mathematics, $x 1617-9692 ; $v v. 2315
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.
650 0 $a Convolutions (Mathematics) $3 646444
650 0 $a Differential operators. $3 555718
650 0 $a Diffusion processes. $3 648159
650 1 4 $a Probability Theory. $3 3538789
650 2 4 $a Operator Theory. $3 897311
650 2 4 $a Special Functions. $3 897326
650 2 4 $a Integral Transforms and Operational Calculus. $3 3538804
700 1 $a Guerra, Manuel. $3 3603375
700 1 $a Yakubovich, Semyon. $3 3603376
710 2 $a SpringerLink (Online service) $3 836513
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830 0 $a Lecture notes in mathematics ; $v v. 2315. $3 3603377
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