<abstract xmlns="http://www.w3.org/1999/xhtml">

We consider a Nevanlinna–Pick interpolation problem on finite sequences of the unit disc, constrained by Beurling–Sobolev norms. We find sharp asymptotics of the corresponding interpolation quantities, thereby improving the known estimates. On our way we obtain a S. M. Nikolskii type inequality for rational functions whose poles lie outside of the unit disc. It shows that the embedding of the Hardy space <italic>H</italic>2 into the Wiener algebra of absolutely convergent Fourier/Taylor series is invertible on the subset of rational functions of a given degree, whose poles remain at a given distance from the unit circle.
</abstract>

We consider a Nevanlinna–Pick interpolation problem on finite sequences of the unit disc, constrained by Beurling–Sobolev norms. We find sharp asymptotics of the corresponding interpolation quantities, thereby improving the known estimates. On our way we obtain a S. M. Nikolskii type inequality for rational functions whose poles lie outside of the unit disc. It shows that the embedding of the Hardy space H2 into the Wiener algebra of absolutely convergent Fourier/Taylor series is invertible on the subset of rational functions of a given degree, whose poles remain at a given distance from the unit circle.

<italic>H</italic>∞ interpolation constrained by Beurling–Sobolev norms

Laboratoire ADEF, Campus Universitaire de Saint-Jérôme

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

 interpolation constrained by Beurling–Sobolev norms

We consider a Nevanlinna–Pick interpolation problem on finite sequences of the unit disc, constrained by Beurling–Sobolev norms. We find sharp asymptotics of...

H^∞ interpolation constrained by Beurling–Sobolev norms

Published Online: Jun 07, 2023

Page range: 157 - 167

Received: Oct 31, 2022

Accepted: Jan 16, 2023

DOI: https://doi.org/10.2478/mjpaa-2023-0012

Keywords
interpolation, Blaschke product, Model space, Rational function, Hardy spaces, Wiener algebra, Beurling–Sobolev spaces

© 2023 Anton Baranov et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

H∞ interpolation constrained by Beurling–Sobolev norms

Published Online: Jun 07, 2023

Page range: 157 - 167

Received: Oct 31, 2022

Accepted: Jan 16, 2023

DOI: https://doi.org/10.2478/mjpaa-2023-0012

Keywordsinterpolation, Blaschke product, Model space, Rational function, Hardy spaces, Wiener algebra, Beurling–Sobolev spaces

© 2023 Anton Baranov et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

H^∞ interpolation constrained by Beurling–Sobolev norms

Keywords
interpolation, Blaschke product, Model space, Rational function, Hardy spaces, Wiener algebra, Beurling–Sobolev spaces