Fourier transform of a Gaussian measure on the Heisenberg group
arXiv:math/0511016 · doi:10.1016/j.anihpb.2005.07.002
Abstract
An explicit formula is derived for the Fourier transform of a Gaussian measure on the Heisenberg group at the Schrodinger representation. Using this explicit formula, necessary and sufficient conditions are given for the convolution of two Gaussian measures to be a Gaussian measure.
38 pages, completed version