Matrix representation of Toeplitz operators on Newton spaces

In this paper, we study several properties of an orthonormal basis $\{N_n(z)\}$ $\{N_{n}(z)\}$ for the Newton space $N^2(\mathbb{P})$ $N^{2}({\mathbb{P}})$ . In particular, we investigate the product of $N_m$ $N_{m}$ and $N_m$ $N_{m}$ and the orthogonal projection P of $\overline{N_n}{N}_m$ $\overline{N_{n}}N_{m}$ that maps from $L^2(\mathbb{P})$ $L^{2}(\mathbb{P})$ onto $N^2(\mathbb{P})$ $N^{2}(\mathbb{P})$ . Moreover, we find the matrix representation of Toeplitz operators with respect to such an orthonormal basis on the Newton space $N^2(\mathbb{P})$ $N^{2}({\mathbb{P}})$ .