Likewise theta functions of rank $r$ on $\mathbb{R}^d$: analytic   properties and associated Segal-Bargmann transform
  We introduce and study the Hilbert space of $(L^2,\Gamma,\chi)$-likewise theta functions on $\mathbb{R}^d$ with respect to a given discrete subgroup $\Gamma$ of arbitrary rank and a character $\chi$ of $\Gamma$. 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. 
A. Ghanmi, A. Intissar, Z. Mouhcine, and M. Ziyat
math.CV