Convolution-like Structures, Differential Operators and Diffusion Processes

Rúben Sousa, Manuel Guerra, Semyon Yakubovich (Autoren)

Buch | Softcover

XII, 262 Seiten

2022 | 1st ed. 2022
Springer International Publishing (Verlag)
978-3-031-05295-8 (ISBN)

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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 X_t 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 X_t 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.

- 1. Introduction. - 2. Preliminaries. - 3. The Whittaker Convolution. - 4. Generalized Convolutions for Sturm-Liouville Operators. - 5. Convolution-Like Structures on Multidimensional Spaces.

Erscheinungsdatum	29.07.2022
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XII, 262 p. 1 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	427 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	integral transforms • ordinary and partial differential equations • Special Functions • spectral theory • Stochastic Processes
ISBN-10	3-031-05295-1 / 3031052951
ISBN-13	978-3-031-05295-8 / 9783031052958
Zustand	Neuware