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Convolution-like Structures, Differential Operators and Diffusion Processes (Lecture Notes in Mathematics, Band 2315) - Softcover

Sousa, Rúben; Guerra, Manuel; Yakubovich, Semyon

 
9783031052958: Convolution-like Structures, Differential Operators and Diffusion Processes (Lecture Notes in Mathematics, Band 2315)
Softcover
ISBN 10: 3031052951 ISBN 13: 9783031052958
Verlag: Springer, 2022

Inhaltsangabe

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.

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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.

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
Springer
Erscheinungsdatum
2022
Sprache
Englisch
ISBN 10 
3031052951
ISBN 13 
9783031052958
Einband
Taschenbuch
Auflage
1
Anzahl der Seiten
276
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