Composition operators on the Newton space |
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Authors: | Gordon MacDonald Peter Rosenthal |
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Affiliation: | a Department of Mathematics and Statistics, University of Prince Edward Island, Charlottetown, PEI, C1A 4P3, Canada b Department of Mathematics, University of Toronto, Toronto, ON, M5S 3G3, Canada |
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Abstract: | We investigate properties of composition operators C? 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 C? with respect to the basis of Newton polynomials in terms of the value of the symbol ? at the non-negative integers. We also establish conditions on the symbol ? for boundedness, compactness, and self-adjointness of the induced composition operator C?. 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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Keywords: | Newton space Hilbert space Composition operator |
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