Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4591026 | Journal of Functional Analysis | 2011 | 23 Pages |
Abstract
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.
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