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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)… Click to show full 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.
Keywords:
bargmann transforms;
true bargmann;
automorphic functions;
rank one;
transforms rank
Journal Title: Journal of Mathematical Physics
Year Published: 2017
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Journal Title: Journal of Mathematical Physics
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!