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.