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＜電子ブック＞
Convolution-like Structures, Differential Operators and Diffusion Processes / by Rúben Sousa, Manuel Guerra, Semyon Yakubovich
(Lecture Notes in Mathematics. ISSN:16179692 ; 2315)

版	1st ed. 2022.
出版者	Cham : Springer International Publishing : Imprint: Springer
出版年	2022
本文言語	英語
大きさ	XII, 262 p. 1 illus. in color : online resource
冊子体	Convolution-like structures, differential operators and diffusion processes / Rúben Sousa, Manuel Guerra, Semyon Yakubovich ; : pbk
著者標目	*Sousa, Rúben author Guerra, Manuel author Yakubovich, Semyon author SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Operator theory LCSH:Special functions LCSH:Mathematical analysis FREE:Probability Theory FREE:Operator Theory FREE:Special Functions FREE:Integral Transforms and Operational Calculus
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-031-05296-5

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