Rank of Truncated Toeplitz Operators

We establish concrete rank formulas for a class of finite rank truncated Toeplitz operators on the model spaces Ku2:=H2⊖uH2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K^2_u:= H^2 \ominus uH^2$$\end{document} in terms of their symbol functions. We also establish some rank inequalities for truncated Toeplitz operators on finite dimensional model spaces.