Matrix representation of Toeplitz operators on Newton spaces

Abstract

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 ( P ) . In particular, we investigate the product of $N_{m}$ N m and $N_{m}$ N m and the orthogonal projection P of $\overline{N_{n}}N_{m}$ N n ‾ N m that maps from $L^{2}(\mathbb{P})$ L 2 ( P ) onto $N^{2}(\mathbb{P})$ N 2 ( 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 ( P ) .