Concrete description of the (Г, χ)-theta Fock-Bargmann space for rank one in high dimension

DOI10.1080/17476933.2015.1047834zbMath1327.32010arXiv1403.3815OpenAlexW1959523455MaRDI QIDQ3455416

Mohammed Souid El Ainin

Publication date: 4 December 2015

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.3815

zbMATH Keywords

theta functionorthonormal basisreproducing kernelFock-Bargmann space on \(\mathbb C^g\)

Mathematics Subject Classification ID

Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) (32A37)

Related Items (4)

True Bargmann transforms for rank one automorphic functions associated with Landau levels ⋮ On holomorphic theta functions associated with rank \(r\) isotropic discrete subgroups ⋮ Complex creation operator and planar automorphic functions ⋮ On a novel class of polyanalytic Hermite polynomials

Cites Work

• Tata lectures on theta. I: Introduction and motivation: Theta functions in one variable. Basic results on theta functions in several variables. With the assistance of C. Musili, M. Nori, E. Previato, and M. Stillman
• Compact Heisenberg manifolds as CR manifolds
• On a Hilbert space of analytic functions and an associated integral transform part I
• On the dimension of the space of theta functions
• Construction of concrete orthonormal basis for (L2, Γ, χ)-theta functions associated to discrete subgroups of rank one in $({\mathbb {C}},+)$(C,+)
• A short note on the chaoticity of a weight shift on concrete orthonormal basis associated to some Fock-Bargmann space
• Landau automorphic functions on Cn of magnitude ν

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