Concrete description for rank one (Γ, χ)-theta Fock-Bargmann space in high dimension

2014/03/15 by Mohammed Souid El Ainin, Ainin, Mohammed Souid El
Mathematics · #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.CV #math.FA

paper · pdf · doi:10.48550/arxiv.1403.3815

10 pages

arxiv created 2014/03/15 · openalex publication_date 2014/03/15 · arxiv updated 2014/03/18 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

We deal with the (ℤω, χ)-theta Fock-Bargmann space consisting of holomorphic automorphic functions associated to given discrete subgroup in ℂ^g of rank one and given character χ. We give concrete description of its elements, it looks like a tensor product of a theta Fock-Bargmann space on the complex plane ℂ and the classical Fock-Bargmann space on ℂ^g-1. Moreover, we construct an orthonormal basis and we give explicit expression of its reproducing kernel function in terms of Riemann theta function.

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