Discrete and Continuous Signals: Analysis, Information and Applications

Left-invariant diffusions on compact groups through Dirichlet form perturbation

12 Dec 2023, 15:00

35m

St. Petersburg University, MCS faculty

Speaker

Qi Hou (Beijing Institute of Mathematical Sciences and Applications)

Description

Gaussian convolution semigroups (also called heat semigroups) on infinite dimensional compact groups exhibit a rich variety of analytic properties. The current knowledge mostly restricts to the product or central types, corresponding to bi-invariant diffusions. In this talk we explain how to obtain heat kernel information for certain (non-product-type, noncentral) Gaussian semigroups through Dirichlet form perturbations. They correspond to certain left-invariant elliptic or sub-elliptic diffusions on compact groups, with generators left-invariant (sub-)Laplacians. This is based on joint work with Laurent Saloff-Coste.