On $m$-isometric Toeplitz operators

In this paper, we study $m$-isometric Toeplitz operators $T_{\varphi}$ with rational symbols. We characterize $m$-isometric Toeplitz operators $T_{\varphi}$ by properties of the rational symbols $\varphi$. In addition, we give a necessary and sufficient condition for Toeplitz operators $T_{\varphi}$ with analytic symbols $\varphi$ to be $m$-expansive or $m$-contractive. Finally, we give some results for $m$-expansive and $m$-contractive Toeplitz operators $T_{\varphi}$ with trigonometric polynomial symbols $\varphi$.