Remarks on Composition Operators on the Newton Space

Abstract

In this paper, we study properties of composition operators on the Newton space, i.e., the Hilbert space of analytic functions which have the Newton polynomials as an orthonormal basis. In particular, we focus on various properties of the composition operator C-T induced by T on the Newton space where T(z) = z + 1. Moreover, we examine conditions on the symbol phi for the induced composition operator C-phi which belongs to Newton space N-2 (P) where phi is a linear fraction transformation or an analytic function of P. Finally, we concern complex symmetric composition operators on the Newton space N-2 (P).