Matrix representation of Toeplitz operators on Newton spaces

Abstract

Abstract In this paper, we study several properties of an orthonormal basis { N n ( z ) } $\{N_{n}(z)\}$ for the Newton space N 2 ( 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 N n ‾ N m $\overline{N_{n}}N_{m}$ that maps from L 2 ( P ) $L^{2}(\mathbb{P})$ onto N 2 ( 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 ( P ) $N^{2}({\mathbb{P}})$ .

Keywords

• Newton space
• Newton polynomials
• The matrix of Toeplitz operator