Constructive polynomial approximation in Banach spaces of holomorphic functions | Vidéo | Carmin.tv

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Constructive polynomial approximation in Banach spaces of holomorphic functions

By Thomas Ransford

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

Let $X$ be a Banach space of holomorphic functions on the unit disk. A linear polynomial approximation scheme for $X$ is a sequence of bounded linear operators $T_{n} :X\rightarrow X$ with the property that, for each $f\in X$, the functions $T_{n}\left ( f \right )$ are polynomials converging to $f$ in the norm of the space. We completely characterize those spaces $X$ that admit a linear polynomial approximation scheme. In particular, we show that it is not sufficient merely that polynomials be dense in $X$. (Joint work with Javad Mashreghi).

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.19579503
Cite this video Ransford, Thomas (21/11/2019). Constructive polynomial approximation in Banach spaces of holomorphic functions. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19579503
URL https://dx.doi.org/10.24350/CIRM.V.19579503

Domain(s)

Bibliography

MASHREGHI, Javad et RANSFORD, Thomas. Linear polynomial approximation schemes in Banach holomorphic function spaces. Analysis and Mathematical Physics, 2019, vol. 9, p. 899-905. - https://doi.org/10.1007/s13324-019-00312-y
EL-FALLAH, Omar, FRICAIN, Emmanuel, KELLAY, Karim, et al. Constructive approximation in de Branges–Rovnyak spaces. Constructive Approximation, 2016, vol. 44, no 2, p. 269-281. - https://doi.org/10.1007/s00365-015-9312-4

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