FrançaisPerturbations of the holomorphic functional calculus: differential operators versus general sectorial operators
Post-edited
Authors : Portal, Pierre (Author of the conference)
CIRM (Publisher )
42B30 - $H^p$-spaces
47A60 - Functional calculus
47F05 - Partial differential operators [See also 35Pxx, 58Jxx]
42B37 - Harmonic analysis and PDE
CIRM (Publisher )
Abstract :
Nigel Kalton played a prominent role in the development of a holomorphic functional calculus for unbounded sectorial operators. He showed, in particular, that such a calculus is highly unstable under perturbation: given an operator $D$ with a bounded functional calculus, fairly stringent conditions have to be imposed on a perturbation $B$ for $DB$ to also have a bounded functional calculus. Nigel, however, often mentioned that, while these results give a fairly complete picture of what is true at a pure operator theoretic level, more should be true for special classes of differential operators. In this talk, I will briefly review Nigel's general results before focusing on differential operators with perturbed coefficients acting on $L_p(\mathbb{R}^{n})$. I will present, in particular, recent joint work with $D$. Frey and A. McIntosh that demonstrates how stable the functional calculus is in this case. The emphasis will be on trying, as suggested by Nigel, to understand what makes differential operators so special from an operator theoretic point of view.
MSC Codes : 42B30 - $H^p$-spaces
47A60 - Functional calculus
47F05 - Partial differential operators [See also 35Pxx, 58Jxx]
42B37 - Harmonic analysis and PDE
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Information on the Video
Language : EnglishAvailable date : 21/01/15 Conference Date : 13/01/15 Subseries : Research talks arXiv category : Functional Analysis ; Analysis of PDEs Mathematical Area(s) : Analysis and its Applications Format : QuickTime (.mov) Video Time : 01:02:22 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2015-01-13_Portal.mp4 
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Information on the Event
Event Title : Banach spaces and their applications in analysis / Espaces de Banach et applications à l'analyseEvent Organizers : Albiac, Fernando ; Casazza, Peter G. ; Godefroy, Gilles ; Lancien, Gilles Dates : 12/01/15 - 16/01/15 Event Year : 2015
Citation Data
DOI : 10.24350/CIRM.V.18665003Cite this video as: Portal, Pierre (2015). Perturbations of the holomorphic functional calculus: differential operators versus general sectorial operators. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18665003 URI : http://dx.doi.org/10.24350/CIRM.V.18665003 |
Bibliography
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