@article{1448484,
      recid = {1448484},
      author = {Sousa, Rúben and Guerra, Manuel. and Yakubovich, S. B.},
      title = {Convolution-like structures, differential operators and  diffusion processes /},
      publisher = {Springer,},
      address = {Cham :},
      pages = {1 online resource (269 pages)},
      year = {2022},
      note = {5.4.5 Product Formulas and Convolutions Associated with  Elliptic Operators on Subsets of R2},
      abstract = {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.},
      url = {http://library.usi.edu/record/1448484},
      doi = {https://doi.org/10.1007/978-3-031-05296-5},
}