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H ∞ Interpolation and Embedding Theorems for Rational Functions. / Baranov, Anton; Zarouf, Rachid.

In: Integral Equations and Operator Theory, Vol. 91, No. 3, 18, 01.06.2019.

Research output: Contribution to journal › Article › peer-review

Harvard

Baranov, A & Zarouf, R 2019, 'H ∞ Interpolation and Embedding Theorems for Rational Functions', Integral Equations and Operator Theory, vol. 91, no. 3, 18. https://doi.org/10.1007/s00020-019-2514-6

APA

Baranov, A., & Zarouf, R. (2019). H ∞ Interpolation and Embedding Theorems for Rational Functions. Integral Equations and Operator Theory, 91(3), [18]. https://doi.org/10.1007/s00020-019-2514-6

Vancouver

Baranov A, Zarouf R. H ∞ Interpolation and Embedding Theorems for Rational Functions. Integral Equations and Operator Theory. 2019 Jun 1;91(3). 18. https://doi.org/10.1007/s00020-019-2514-6

Author

Baranov, Anton ; Zarouf, Rachid. / H ∞ Interpolation and Embedding Theorems for Rational Functions. In: Integral Equations and Operator Theory. 2019 ; Vol. 91, No. 3.

BibTeX

@article{49e24498250548cc887f354bf971bd77,
title = "H ∞ Interpolation and Embedding Theorems for Rational Functions",
abstract = " We consider a Nevanlinna–Pick interpolation problem on finite sequences of the unit disc D constrained by Hardy and radial-weighted Bergman norms. We find sharp asymptotics on the corresponding interpolation constants. As another application of our techniques we prove embedding theorems for rational functions. We find that the embedding of H ∞ into Hardy or radial-weighted Bergman spaces in D is invertible on the subset of rational functions of a given degree n whose poles are separated from the unit circle and obtain asymptotically sharp estimates of the corresponding embedding constants. ",
keywords = "Blaschke product, H interpolation, Hardy spaces, Model space, Rational function, Weighted Bergman spaces, H-infinity interpolation, INEQUALITIES, MAXIMUM, MATRICES, HARDY",
author = "Anton Baranov and Rachid Zarouf",
year = "2019",
month = jun,
day = "1",
doi = "10.1007/s00020-019-2514-6",
language = "English",
volume = "91",
journal = "Integral Equations and Operator Theory",
issn = "0378-620X",
publisher = "Birkh{\"a}user Verlag AG",
number = "3",

}

RIS

TY - JOUR

T1 - H ∞ Interpolation and Embedding Theorems for Rational Functions

AU - Baranov, Anton

AU - Zarouf, Rachid

PY - 2019/6/1

Y1 - 2019/6/1

N2 - We consider a Nevanlinna–Pick interpolation problem on finite sequences of the unit disc D constrained by Hardy and radial-weighted Bergman norms. We find sharp asymptotics on the corresponding interpolation constants. As another application of our techniques we prove embedding theorems for rational functions. We find that the embedding of H ∞ into Hardy or radial-weighted Bergman spaces in D is invertible on the subset of rational functions of a given degree n whose poles are separated from the unit circle and obtain asymptotically sharp estimates of the corresponding embedding constants.

AB - We consider a Nevanlinna–Pick interpolation problem on finite sequences of the unit disc D constrained by Hardy and radial-weighted Bergman norms. We find sharp asymptotics on the corresponding interpolation constants. As another application of our techniques we prove embedding theorems for rational functions. We find that the embedding of H ∞ into Hardy or radial-weighted Bergman spaces in D is invertible on the subset of rational functions of a given degree n whose poles are separated from the unit circle and obtain asymptotically sharp estimates of the corresponding embedding constants.

KW - Blaschke product

KW - H interpolation

KW - Hardy spaces

KW - Model space

KW - Rational function

KW - Weighted Bergman spaces

KW - H-infinity interpolation

KW - INEQUALITIES

KW - MAXIMUM

KW - MATRICES

KW - HARDY

UR - http://www.scopus.com/inward/record.url?scp=85064207075&partnerID=8YFLogxK

U2 - 10.1007/s00020-019-2514-6

DO - 10.1007/s00020-019-2514-6

M3 - Article

AN - SCOPUS:85064207075

VL - 91

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

IS - 3

M1 - 18

ER -

ID: 42796529