Toeplitz Operators with Unbounded Symbols on Segal-Bargmann Space

Abstract:

      In this paper, we construct a function $\varphi$ in $L^{2}(\mathbb{C}^{n},\d V_{\alpha})$ which is unbounded on any neighborhood of each point in $\mathbb{C}^{n}$ such that $T_{\varphi}$ is a trace class operator on the Segal-Bargmann space $H^{2}(\mathbb{C}^{n},\d V_{\alpha})$. In addition, we also characterize the Schatten $p$-class Toeplitz operators with positive measure symbols on $H^{2}(\mathbb{C}^{n},\d V_{\alpha})$.