On the relative fundamental solutions for a second order differential operator on the Heisenberg group (Q2717570)

The relative fundamental solutions are computed explicitly for a second order differential operator written in terms of the \(p+q=n\) generators forming the standard basis of the Lie algebra of the \((2n+1)\)-dimensional Heisenberg group \(H_n\). The work is based on previous results concerning the existence of the above mentioned solutions for the differential equations of the type considered (1990, 1992, Müller, Ricci) as well as the solution computed for the case \(q=0\) (1973, Folland). In the framework of this approach, the Hermite temporal distributions associated to the group \(U(p,q)\) (1998, Folland) and the related spectral decomposition on the Heisenberg group (2000, Godoy, Saal) are essentially exploited.