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Convolution-like Structures, Differential Operators and Diffusion Processes (Lecture Notes in Mathematics) - Softcover

Sousa, Rúben; Guerra, Manuel; Yakubovich, Semyon

 
9783031052958: Convolution-like Structures, Differential Operators and Diffusion Processes (Lecture Notes in Mathematics)
Softcover
ISBN 10: 3031052951 ISBN 13: 9783031052958
Publisher: Springer, 2022

Synopsis

T​his 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.

"synopsis" may belong to another edition of this title.

About the Author


From the Back Cover

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.

"About this title" may belong to another edition of this title.

Publisher
Springer
Publication date
2022
Language
English
ISBN 10 
3031052951
ISBN 13 
9783031052958
Binding
Paperback
Edition number
1
Number of pages
276