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October, 2021 Concrete $L^2$-spectral Analysis of a Bi-weighted $\Gamma$-automorphic Twisted Laplacian
Aymane El Fardi, Allal Ghanmi, Ahmed Intissar
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Taiwanese J. Math. 25(5): 887-904 (October, 2021). DOI: 10.11650/tjm/210401

Abstract

We consider a twisted Laplacian $\Delta_{\nu,\mu}$ on the $n$-complex space associated with the sub-Laplacian of the Heisenberg group $\mathbb{C} \times_{\omega} \mathbb{C}^n$ realized as a central extension of the real Heisenberg group $H_{2n+1}$. The main results to which is aimed this paper concern the spectral theory of $\Delta_{\nu,\mu}^{\Gamma}$ when acting on some $L^2$ space of $\Gamma$-automorphic functions of biweight $(\nu,\mu)$ associated to given cocompat discrete subgroup $\Gamma$ of the additive group $\mathbb{C}^n$. We describe its spectrum proving a stability theorem. Using the Selberg's approach, we give the explicit dimension formula for the corresponding $L^2$-eigenspaces. We also construct a concrete basis of such $L^2$-eigenspaces.

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Aymane El Fardi. Allal Ghanmi. Ahmed Intissar. "Concrete $L^2$-spectral Analysis of a Bi-weighted $\Gamma$-automorphic Twisted Laplacian." Taiwanese J. Math. 25 (5) 887 - 904, October, 2021. https://doi.org/10.11650/tjm/210401

Information

Received: 18 November 2020; Accepted: 6 April 2021; Published: October, 2021
First available in Project Euclid: 20 April 2021

Digital Object Identifier: 10.11650/tjm/210401

Subjects:
Primary: 11E45, 11F03
Secondary: 14K25, 32N05

Rights: Copyright © 2021 The Mathematical Society of the Republic of China

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Vol.25 • No. 5 • October, 2021
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