Interpolation in Spaces of Analytic Functions / Interpolation dans les espaces de fonctions analytiques

Collection Interpolation in Spaces of Analytic Functions / Interpolation dans les espaces de fonctions analytiques

Organizer(s) Fricain, Emmanuel ; Hartmann, Andreas ; Wick, Brett

Date(s) 18/11/2019 - 22/11/2019

linked URL https://conferences.cirm-math.fr/2055.html

00:00:00 / 00:00:00

4 5

The Szegö minimum problem

By Alexander Borichev

weighted polynomial approximation

Given a finite positive measure $\mu$ on the unit circle, we consider the distance $e_{n}\left ( \mu \right )$ from $z^{n}$ to the analytic polynomials of degree less than $n$ in $L^{2}\left ( \mu \right )$. We study the asymptotic behavior of $e_{n}\left ( \mu \right )$ for $n\rightarrow \infty$ when the logarithmic integral of the density of $\mu$ diverges for different classes of measures $\mu$.

Information about the video

Date of recording 21/11/2019
Date of publication 13/12/2019
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19579003
Cite this video Borichev, Alexander (21/11/2019). The Szegö minimum problem. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19579003
URL https://dx.doi.org/10.24350/CIRM.V.19579003

Domain(s)

Complex Variables

Bibliography

BORICHEV, Alexander, KONONOVA, Anna, et SODIN, Mikhail. Notes on the Szego minimum problem. I. Measures with deep zeroes. arXiv preprint arXiv:1902.00874, 2019. - https://arxiv.org/abs/1902.00874
BORICHEV, Alexander, KONONOVA, Anna, et SODIN, Mikhail. Notes on the Szego minimum problem. II. Singular measures. arXiv preprint arXiv:1902.00872, 2019. - https://arxiv.org/abs/1902.00872

MSC codes

42C05 Orthogonal functions and polynomials, general theory

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