Publication:
Remarks on Inner Functions and Optimal Approximants

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URI: https://hdl.handle.net/10016/32630
ISSN: 0008-4395
DOI: https://doi.org/10.4153/CMB-2017-058-4
UXXI: AR/0000026418
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Remarks_CMB_2018_ps.pdf (595.68 KB)
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2018-12-01
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Cambridge University Press
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Abstract
We discuss the concept of inner function in reproducing kernelHilbert 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 modiûed to produce inner functions.
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Inner function, Reproducing kernel hilbert space, Operator theoretic function theory
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Bénéteau, C., Fleeman, M. C., Khavinson, D. S., Seco, D. & Sola, A. A. (2018). Remarks on Inner Functions and Optimal Approximants. Canadian Mathematical Bulletin, 61(4), pp. 704–716.
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