Remarks on Inner Functions and Optimal Approximants

Bénéteau, Catherine ; Fleeman, Matthew C. ; Khavinson, Dmitry S. ; Seco, Daniel ; Sola, Alan A.

Canadian mathematical bulletin, Tome 61 (2018) no. 4, pp. 704-716

Résumé

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.

Détail

DOI : 10.4153/CMB-2017-058-4

Mots-clés : 46E22, 30J05, inner function, reproducing kernel hilbert space, operator-theoretic function theory

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