Matrix representation of Toeplitz operators on Newton spaces

In this paper, we study several properties of an orthonormal basis ₙ(z)\ { N n ( z ) } for the Newton space N²(P) N 2 ( P ) . In particular, we investigate the product of Nₘ N m and Nₘ N m and the orthogonal projection P of NₙNₘ N n ‾ N m that maps from L²(P) L 2 ( P ) onto N²(P) N 2 ( P ) . Moreover, we find the matrix representation of Toeplitz operators with respect to such an orthonormal basis on the Newton space N²(P) N 2 ( P ) .