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arXiv · 1403.3815

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

Mohammed Souid El Ainin
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Abstract

We deal with the $(\mathbb{Z}ω, χ)$-theta Fock-Bargmann space consisting of holomorphic automorphic functions associated to given discrete subgroup in $\mathbb{C}^g$ 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 $\mathbb{C}$ and the classical Fock-Bargmann space on $\mathbb{C}^{g-1}$. 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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Mohammed Souid El Ainin. 2014-03-15. Concrete description for rank one $(Γ, χ)$-theta Fock-Bargmann space in high dimension. https://arxiv.org/abs/1403.3815

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