Geodesic
Remarks on Inner Functions and Optimal Approximants
Canadian mathematical bulletin, Tome 61 (2018) no. 4, pp. 704-716

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DOI

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.
DOI : 10.4153/CMB-2017-058-4
Mots-clés : 46E22, 30J05, inner function, reproducing kernel hilbert space, operator-theoretic function theory 
Bénéteau, Catherine; Fleeman, Matthew C.; Khavinson, Dmitry S.; Seco, Daniel; Sola, Alan A. Remarks on Inner Functions and Optimal Approximants. Canadian mathematical bulletin, Tome 61 (2018) no. 4, pp. 704-716. doi: 10.4153/CMB-2017-058-4
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     author = {B\'en\'eteau, Catherine and Fleeman, Matthew C. and Khavinson, Dmitry S. and Seco, Daniel and Sola, Alan A.},
     title = {Remarks on {Inner} {Functions} and {Optimal} {Approximants}},
     journal = {Canadian mathematical bulletin},
     pages = {704--716},
     year = {2018},
     volume = {61},
     number = {4},
     doi = {10.4153/CMB-2017-058-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-058-4/}
}
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%J Canadian mathematical bulletin
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