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arXiv · 1707.06166

Remarks on Inner Functions and Optimal Approximants

Catherine Bénéteau·Matthew Fleeman·Dmitry Khavinson·Daniel Seco·Alan Sola
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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.

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Catherine Bénéteau, Matthew Fleeman, Dmitry Khavinson, Daniel Seco, Alan Sola. 2017-07-19. Remarks on Inner Functions and Optimal Approximants. https://doi.org/10.4153/cmb-2017-058-4

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