Ahmedou Yahya ould Mohameden

An intertwining operator for the harmonic oscillator and the Dirac operator with application to the heat and wave kernels

In this article an intertwining operator is constructed which transforms the harmonic oscillator to the Dirac operator (the first order derivative operator). We give also the explicit solutions to the heat and wave equation associated to Dirac operator. As an application the heat and the wave kernels of the harmonic oscillator are computed.