Mathematics

Riesz transforms are a family of generalization of Hilbert transformation in one-dimensional space to n-dimensional space. They also are singular integral operators which are given by a convolution with the kernels having a singularity at the origin. At the seminar I will present probabilistic representations of Riesz transforms (Gundy-Varopoulos-Silverstein's background radiation and Bass' approach) and a new probabilistic representation of iterated Riesz transforms in the context of the Helmholtz-Hodge decomposition.