Spectral analysis on planar mixed automorphic forms

We introduce and we carry out some concrete spectral properties of a class of magnetic Schrödinger operators leaving invariant the space of the planar mixed automorphic forms of type ( ν , μ ) with respect to an equivariant pair ( ρ , τ ) and given lattice Γ ⊂ C . The associated polynomials constitute classes of generalized complex polynomials of Hermite type.