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Zhengyuan Zhuo, Conghui Shen, Dongxing Li, Songxiao Li, A Hankel matrix acting on Fock spaces

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DOI: 10.23952/jnva.7.2023.2.05

Volume 7, Issue 2, 1 April 2023, Pages 235-250


Abstract. Let \nu be a positive Borel measure on the interval [0,\infty). Let \mathcal{H}_\nu=(\nu_{n,k})_{n,k\geq 0} be the Hankel matrix with entries \nu_{n,k}=\int_{[0,\infty)}\frac{ t^{n+k}}{n!}\,d\nu(t). The matrix \mathcal{H}_\nu induces formally the operator \mathcal{H}_\nu(f)(z)=\sum_{n=0}^{\infty}(\sum_{k=0}^{\infty}\nu _{n,k}a_k)z^n on the space of all entire functions f(z) =\sum_{n=0}^{\infty} a_n z^n. In this paper, we investigate those positive Borel measures such that \mathcal{H}_\nu(f)(z)=\int_{[0, \infty)}f(t)e^{t z}\,d\nu(t), z\in \mathbb{C} for all f\in F^p, and among them we characterize those for which \mathcal{H}_\nu is a bounded (resp., compact) operator from the Fock space F^p into the space F^q (0\textless p,q\textless\infty).


How to Cite this Article:
Z. Zhuo, C. Shen, D. Li, S. Li, A Hankel matrix acting on Fock spaces, J. Nonlinear Var. Anal. 7 (2023), 235-250.