On spectral analysis of a magnetic Schrodinger operator on planar mixed automorphic forms

We characterize the space of the so-called planar mixed automorphic forms of type $(\nu,\mu)$ with respect to an equivariant pair $(\rho,\tau)$ as the image of the usual automorphic forms by an appropriate transform and we investigate some concrete basic spectral properties of a magnetic Schrodinger operator acting on them. The associated polynomials constitute classes of generalized complex polynomials of Hermite type.Comment: 10 pages. This is a substantially reorganized, revised and improved exposition. Misprints corrected and references added. Submitte

A characterization of planar mixed automorphic forms

We characterize the space of the so-called planar mixed automorphic forms of type $(\nu,\mu)$ with respect to an equivariant pair $(\rho,\tau)$ as the image, by an appropriate transform, of the usual (Landau) automorphic forms involving special multiplier.Comment: The main result is in fact contained in a previous paper (arXiv.org:0708.3357). The actual version is written without the use the spectral theory of the differential operator involved in such paper