Date:	Wed, March 2, 2011
Time:	14:15
Place:	Research I Seminar Room

Abstract: We introduce hierarchical Weyl transforms based on multilinear Wigner transforms, develop for them the analogs of the basic properties of the classic Weyl transforms, which are then used to compute the heat semi- group of a hierarchical twisted Laplacian. We prove that the hierarchical twisted Laplacian is unitarily equivalent to the the tensor product of the one-dimensional Hermite operator and the identity operator on $L^2(R^{m+1})$, and we use this unitarily equivalence to show that $L_m$ is globally hypoel- liptic in the Schwartz space.