TY  - GEN
N2  - 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.
DO  - 10.1007/978-3-031-05296-5
DO  - doi
AB  - 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.
T1  - Convolution-like structures, differential operators and diffusion processes /
DA  - 2022.
CY  - Cham :
AU  - Sousa, Rúben
AU  - Guerra, Manuel.
AU  - Yakubovich, S. B.
VL  - v. 2315
CN  - QA601
PB  - Springer,
PP  - Cham :
PY  - 2022.
N1  - 5.4.5 Product Formulas and Convolutions Associated with Elliptic Operators on Subsets of R2
ID  - 1448484
KW  - Convolutions (Mathematics)
KW  - Differential operators.
KW  - Diffusion processes.
SN  - 9783031052965
SN  - 303105296X
TI  - Convolution-like structures, differential operators and diffusion processes /
LK  - https://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-05296-5
UR  - https://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-05296-5
ER  -