English
Perturbations of the holomorphic functional calculus: differential operators versus general sectorial operators
Post-edited
Auteurs : Portal, Pierre (Auteur de la Conférence)
CIRM (Editeur )
42B30 - $H^p$-spaces
47A60 - Functional calculus
47F05 - Partial differential operators [See also 35Pxx, 58Jxx]
42B37 - Harmonic analysis and PDE
CIRM (Editeur )
Résumé :
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.
Codes MSC : 42B30 - $H^p$-spaces
47A60 - Functional calculus
47F05 - Partial differential operators [See also 35Pxx, 58Jxx]
42B37 - Harmonic analysis and PDE
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 21/01/15 Date de captation : 13/01/15 Sous collection : Research talks arXiv category : Functional Analysis ; Analysis of PDEs Domaine : Analysis and its Applications Format : QuickTime (.mov) Durée : 01:02:22 Audience : Researchers Download : https://videos.cirm-math.fr/2015-01-13_Portal.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Banach spaces and their applications in analysis / Espaces de Banach et applications à l'analyseOrganisateurs de la rencontre : Albiac, Fernando ; Casazza, Peter G. ; Godefroy, Gilles ; Lancien, Gilles Dates : 12/01/15 - 16/01/15 Année de la rencontre : 2015
Données de citation
DOI : 10.24350/CIRM.V.18665003Citer cette vidéo: 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 |
Bibliographie
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- Hytönen, T., & McIntosch, A. (2010). Stability in p of the $H^{\infty}$-calculus of first-order systems in $L^p$. In A. Hassell, A. McIntosh, & R. Taggart (Eds.), The AMSI-ANU workshop on spectral theory and harmonic analysis. Proceedings of the workshop, Canberra, Australia, July 13–17, 2009 (pp. 167-181). Canberra: Australian National University. (Proceedings of the Centre for Mathematics and its Applications, 44) - https://www.zbmath.org/?q=an:1252.47014
- Hytönen, T., McIntosh, A., & Portal, P. (2008). Kato's square root problem in Banach spaces. Journal of Functional Analysis, 254(3), 675-726 - http://dx.doi.org/10.1016/j.jfa.2007.10.006
- Kalton, N.J. (2007). Perturbations of the $H^{\infty}$-calculus. Collectanea Mathematica, 58(3), 291-325 - https://eudml.org/doc/42036
