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Remarks on Inner Functions and Optimal Approximants (1707.06166v2)
Published 19 Jul 2017 in math.CA, math.CV, and math.FA
Abstract: We discuss the concept of inner function in reproducing kernel Hilbert spaces with an orthogonal basis of monomials and examine connections between inner functions and optimal polynomial approximants to $1/f$, where $f$ is a function in the space. We revisit some classical examples from this perspective, and show how a construction of Shapiro and Shields can be modified to produce inner functions.