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Volume 39, Issue 4
General Optimal Polynomial Approximants, Stabilization, and Projections of Unity

Christopher Felder

DOI: 10.4208/ata.OA-2020-0047

Anal. Theory Appl., 39 (2023), pp. 309-329.

Published online: 2023-12

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  • Abstract

In various Hilbert spaces of analytic functions on the unit disk, we characterize when a function has optimal polynomial approximants given by truncations of a single power series or, equivalently, when the approximants stabilize. We also introduce a generalized notion of optimal approximant and use this to explicitly compute orthogonal projections of 1 onto certain shift invariant subspaces.

  • Keywords

Optimal polynomial approximants, inner functions.

  • AMS Subject Headings

46E22, 0J05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-39-309, author = {Felder , Christopher}, title = {General Optimal Polynomial Approximants, Stabilization, and Projections of Unity}, journal = {Analysis in Theory and Applications}, year = {2023}, volume = {39}, number = {4}, pages = {309--329}, abstract = {

In various Hilbert spaces of analytic functions on the unit disk, we characterize when a function has optimal polynomial approximants given by truncations of a single power series or, equivalently, when the approximants stabilize. We also introduce a generalized notion of optimal approximant and use this to explicitly compute orthogonal projections of 1 onto certain shift invariant subspaces.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2020-0047}, url = {http://global-sci.org/intro/article_detail/ata/22300.html} }
TY - JOUR T1 - General Optimal Polynomial Approximants, Stabilization, and Projections of Unity AU - Felder , Christopher JO - Analysis in Theory and Applications VL - 4 SP - 309 EP - 329 PY - 2023 DA - 2023/12 SN - 39 DO - http://doi.org/10.4208/ata.OA-2020-0047 UR - https://global-sci.org/intro/article_detail/ata/22300.html KW - Optimal polynomial approximants, inner functions. AB -

In various Hilbert spaces of analytic functions on the unit disk, we characterize when a function has optimal polynomial approximants given by truncations of a single power series or, equivalently, when the approximants stabilize. We also introduce a generalized notion of optimal approximant and use this to explicitly compute orthogonal projections of 1 onto certain shift invariant subspaces.

Christopher Felder. (2023). General Optimal Polynomial Approximants, Stabilization, and Projections of Unity. Analysis in Theory and Applications. 39 (4). 309-329. doi:10.4208/ata.OA-2020-0047
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