Likewise theta functions of rank r on ℝ^d: analytic properties and associated Segal-Bargmann transform

2016/03/24 by Allal Ghanmi, Ghanmi, A., Abdelkader Intissar +5
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #Complex Variables (math.CV) #FOS: Mathematics #Primary 32N05 #Secondary 14K25

paper · pdf · doi:10.48550/arxiv.1603.07560

openalex publication_date 2016/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce and study the Hilbert space of (L²,Γ,χ)-likewise theta functions on ℝ^d with respect to a given discrete subgroup Γ of arbitrary rank and a character χ of Γ. A concrete description is given and an orthonormal basis is then constructed. Its range by the classical Segal-Bargmann transform is also characterized and leads to the so-called theta-Bargmann Fock space.

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