Properties of Newton polynomials and Toeplitz operators on Newton spaces

Abstract

In this paper, we study properties of Toeplitz operators on the Newton space N2(H) which has Newton polynomials as an orthonormal basis. We show that for N=(N0,N1,…,Nn)T and m=(1,z,…,zn)T , the equation VUN=m is the transformations between the basis functions which map monomials to Newton polynomials where V and U are given as in Theorem 2.1. Moreover, we consider the truncated Toeplitz operator on N2(H). © 2023, Tusi Mathematical Research Group (TMRG).