Composition operators on the Newton space

We investigate properties of composition operators Cφ on the Newton space (the Hilbert space of analytic functions which have the Newton polynomials as an orthonormal basis).We derive a formula for the entries of the matrix of Cφ with respect to the basis of Newton polynomials in terms of the value of the symbol φ at the non-negative integers. We also establish conditions on the symbol φ for boundedness, compactness, and self-adjointness of the induced composition operator Cφ. A key technique in obtaining these results is use of an isomorphism between the Newton space and the Hardy space via the Binomial Theorem. © 2011 Elsevier Inc. All rights reserved.