A functional calculus on the Heisenberg group and the boundary layer potential square(-1)(+) for the partial derivative-Neumann problem

摘要

There are two natural commuting self-adjoint operators in the enveloping algebra of the Heisenberg group: the Heisenberg sublaplacian Delta(H) and the central element T = -i partial derivative/partial derivative t. The joint spectral theory of these operators is investigated by means of the Laguerre calculus. Explicit convolution kernels are obtained for a large class of functions Phi(-Delta(H), T). In particular we find the kernels of the operators square +,proportional to = root-Delta(H)-proportional to T+T-2 -T that occur in the Kohn solution of the partial derivative-Neumann problem for the associated Siegel domain. (C) 1998 Academic Press. [References: 10]