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.