Abstract
For a given discrete subgroup Γ of (C,+) and given real number ν>0, we study the spectral properties of the magnetic Laplacian operator Δν acting on the Hilbert space LΓ,χ2,ν(C) of (L2,Γ)-automorphic functions (see below for notations). We show that its spectrum is reduced to the eigenvalues νm; m=0,1,…. We also give a concrete description of each eigenspace in terms of the Hermite polynomials. This description will be used to characterize the range of true Bargmann transform of L2-periodic functions on the real line R.
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