Bivariate raising and lowering differential operators for eigenfunctions of a 2D Fourier transform.

We define a two-dimensional (2D) Fourier transform that self-reproduces a one-parameter family of bivariate Hermite functions; these are eigenfunctions of a Hamiltonian differential operator of second order, whose exponential is that transform. We find explicit forms of the bivariate raising and lowering partial differential operators of first degree for the eigenfunctions of this 2D Fourier transform. [ABSTRACT FROM AUTHOR]