Comptes Rendus
no. 8
Complex analysis/Functional analysis
Density of disk algebra functions in de Branges–Rovnyak spaces
[Densité des fonctions dans l'algèbre du disque dans les espaces de de Branges–Rovnyak]

Présenté par : the Editorial Board

Alexandru Aleman1 ; Bartosz Malman1
1 Centre for Mathematical Sciences, Lund University, P.O Box 118, SE-22100 Lund, Sweden
Comptes Rendus. Mathématique, Volume 355 (2017) no. 8, pp. 871-875.

On démontre que les fonctions analytiques dans le disque unité et continues dans le disque fermé sont denses dans l'espace de Branges–Rovnyak généré par un point extrémal de la boule unité de H∞. En utilisant aussi des théorèmes précédents, il résulte que cette classe de fonctions est dense dans un espace de Branges–Rovnyak quelconque.

We prove that functions analytic in the unit disk and continuous up to the boundary are dense in the de Branges–Rovnyak spaces induced by the extreme points of the unit ball of H∞. Together with previous theorems, it follows that this class of functions is dense in any de Branges–Rovnyak space.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.07.015
Alexandru Aleman 1 ; Bartosz Malman 1

1 Centre for Mathematical Sciences, Lund University, P.O Box 118, SE-22100 Lund, Sweden 
@article{CRMATH_2017__355_8_871_0,
     author = {Alexandru Aleman and Bartosz Malman},
     title = {Density of disk algebra functions in de {Branges{\textendash}Rovnyak} spaces},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {871--875},
     publisher = {Elsevier},
     volume = {355},
     number = {8},
     year = {2017},
     doi = {10.1016/j.crma.2017.07.015},
     language = {en},
}
TY  - JOUR
AU  - Alexandru Aleman
AU  - Bartosz Malman
TI  - Density of disk algebra functions in de Branges–Rovnyak spaces
JO  - Comptes Rendus. Mathématique
PY  - 2017
SP  - 871
EP  - 875
VL  - 355
IS  - 8
PB  - Elsevier
DO  - 10.1016/j.crma.2017.07.015
LA  - en
ID  - CRMATH_2017__355_8_871_0
ER  - 
%0 Journal Article
%A Alexandru Aleman
%A Bartosz Malman
%T Density of disk algebra functions in de Branges–Rovnyak spaces
%J Comptes Rendus. Mathématique
%D 2017
%P 871-875
%V 355
%N 8
%I Elsevier
%R 10.1016/j.crma.2017.07.015
%G en
%F CRMATH_2017__355_8_871_0
Alexandru Aleman; Bartosz Malman. Density of disk algebra functions in de Branges–Rovnyak spaces. Comptes Rendus. Mathématique, Volume 355 (2017) no. 8, pp. 871-875. doi : 10.1016/j.crma.2017.07.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.07.015/

[1] A.B. Aleksandrov Invariant subspaces of shift operators. An axiomatic approach, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), Volume 113 (1981), pp. 7-26 (264, English translation in J. Sov. Math., 22, 1983, pp. 1695-1708)

[2] A. Aleman; N.S. Feldman; W.T. Ross The Hardy space of a slit domain, Frontiers in Mathematics, Birkhäuser Verlag, Basel, Switzerland, 2009

[3] A. Aleman; S. Richter; C. Sundberg Beurling's theorem for the Bergman space, Acta Math., Volume 177 (1996), pp. 275-310

[4] S. Banach Theory of Linear Operations, N.-Holl. Math. Libr., vol. 38, North-Holland Publishing Co., Amsterdam, 1987

[5] C. Bénéteau; A. Condori; C. Liaw; W.T. Ross; A. Sola Some open problems in complex and harmonic analysis: report on problem session held during the conference Completeness problems, Carleson measures, and spaces of analytic functions, Recent Progress on Operator Theory and Approximation in Spaces of Analytic Functions, Contemp. Math., vol. 679, American Mathematical Society, Providence, RI, USA, 2016, pp. 207-217

[6] J. Cima; A. Matheson; W.T. Ross The Cauchy Transform, Math. Surv. Monogr., vol. 125, American Mathematical Society, Providence, RI, USA, 2006

[7] O. El-Fallah; E. Fricain; K. Kellay; J. Mashreghi; T. Ransford Constructive approximation in de Branges–Rovnyak spaces, Constr. Approx., Volume 44 (2016), pp. 269-281

[8] V.P. Havin; B. Jöricke The Uncertainty Principle in Harmonic Analysis, Encyclopaedia Math. Sci., vol. 72, Springer, Berlin, 1995

[9] D. Sarason Sub-Hardy Hilbert Spaces in the Unit Disk, Univ. Arkansas Lect. Notes Math. Sci., vol. 10, John Wiley & Sons, Inc., New York, 1994

[10] S.A. Vinogradov Properties of multipliers of integrals of Cauchy–Stieltjes type, and some problems of factorization of analytic functions, Drogobych, 1974, Volume 115 (1976), pp. 5-39 (in Russian); English translation in Transl. Amer. Math. Soc. (2), 1980, pp. 1-32

Cité par Sources :

Commentaires - Politique