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arXiv · 1212.1870

Construction of concrete orthonormal basis for (L^2,Γ,χ)-theta functions associated to discrete subgroups of rank one in (C,+)

Allal Ghanmi·Ahmed Intissar
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Abstract

Let χbe a character on a discrete subgroup Γof rank one of the additive group (C,+). We construct a complete orthonormal basis of the Hilbert space of (L^2,Γ,χ)-theta functions. Furthermore, we show that it possesses a Hilbertian orthogonal decomposition involving the L^2-eigenspaces of the Landau operator Δ_ν; ν>0, associated to the eigenvalues νm. For m=0, the associated L^2-eigenspace is the Hilbert subspace of entire (L^2,Γ,χ)-theta functions. Corresponding orthonormal basis are constructed and the corresponding reproducing kernel can be expressed in terms of the generalized theta function of characteristic [α,0].

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BibTeXRIS

Allal Ghanmi, Ahmed Intissar. 2012-12-09. Construction of concrete orthonormal basis for (L^2,Γ,χ)-theta functions associated to discrete subgroups of rank one in (C,+). https://doi.org/10.1063/1.4811463

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