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Norm-preserving extensions of bounded holomorphic functions
Multi angle
Authors : McCarthy, John (Author of the conference)
CIRM (Publisher )
32-XX - Several complex variables and analytic spaces, {For infinite-dimensional holomorphy, See also 46G20, 58B12}
46-XX - Functional analysis [For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx]
47-XX - Operator theory
CIRM (Publisher )
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Abstract :
Let $V$ be an analytic subvariety of a domain $\Omega$ in $\mathbb{C}^{n}$. When does $V$ have the property that every bounded holomorphic function $f$ on $V$ has an extension to a bounded holomorphic function on $\Omega$ with the same norm?
An obvious sufficient condition is if $V$ is a holomorphic retract of $\Omega$. We shall discuss for what domains $\Omega$ this is also necessary.
This is joint work with Łukasz Kosiński.
Keywords : operator theory; functional analysis; several complex variables
MSC Codes : An obvious sufficient condition is if $V$ is a holomorphic retract of $\Omega$. We shall discuss for what domains $\Omega$ this is also necessary.
This is joint work with Łukasz Kosiński.
Keywords : operator theory; functional analysis; several complex variables
32-XX - Several complex variables and analytic spaces, {For infinite-dimensional holomorphy, See also 46G20, 58B12}
46-XX - Functional analysis [For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx]
47-XX - Operator theory
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 13/12/2019 Conference Date : 18/11/2019 Subseries : Research talks arXiv category : Complex Variables Mathematical Area(s) : Analysis and its Applications Format : MP4 (.mp4) - HD Video Time : 00:36:55 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2019-11-18_McCarthy.mp4 
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Information on the Event
Event Title : Interpolation in Spaces of Analytic Functions / Interpolation dans les espaces de fonctions analytiquesEvent Organizers : Fricain, Emmanuel ; Hartmann, Andreas ; Wick, Brett Dates : 18/11/2019 - 22/11/2019 Event Year : 2019 Event URL : https://conferences.cirm-math.fr/2055.html
Citation Data
DOI : 10.24350/CIRM.V.19579403Cite this video as: McCarthy, John (2019). Norm-preserving extensions of bounded holomorphic functions. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19579403 URI : http://dx.doi.org/10.24350/CIRM.V.19579403 |
See Also
- [Multi angle] Constructive polynomial approximation in Banach spaces of holomorphic functions / Author of the conference Ransford, Thomas.
- [Post-edited] Spectral decompositions and an extension of a theorem of Atzmon: a couple leading to spectral subspaces for Bishop operators / Author of the conference Gallardo-Gutiérrez, Eva A..
- [Multi angle] The Szegö minimum problem / Author of the conference Borichev, Alexander.
- [Multi angle] Singular rational inner functions on the polydisk / Author of the conference Bickel, Kelly.
Bibliography
- KOSIŃSKI, Łukasz et MCCARTHY, John. Norm preserving extensionsof bounded holomorphic functions. Transactions of the American Mathematical Society, 2019, vol. 371, no 10, p. 7243-7257. - https://arxiv.org/abs/1704.03857
