Likewise theta functions of rank $r$ on $\mathbb{R}^d$: analytic properties and associated Segal-Bargmann transform

A. Ghanmi; A. Intissar; Z. Mouhcine; M. Ziyat

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arXiv · 1603.07560

Likewise theta functions of rank $r$ on $\mathbb{R}^d$: analytic properties and associated Segal-Bargmann transform

A. Ghanmi·A. Intissar·Z. Mouhcine·M. Ziyat

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Abstract

We introduce and study the Hilbert space of $(L^2,Γ,χ)$-likewise theta functions on $\mathbb{R}^d$ 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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A. Ghanmi, A. Intissar, Z. Mouhcine, M. Ziyat. 2017-02-02. Likewise theta functions of rank $r$ on $\mathbb{R}^d$: analytic properties and associated Segal-Bargmann transform. https://arxiv.org/abs/1603.07560

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