A Beurling-Carleson set which is a uniqueness set for a given weighted space of analytic functions

Author:
Cyril Agrafeuil

Journal:
Proc. Amer. Math. Soc. **134** (2006), 3287-3294

MSC (2000):
Primary 30C15, 30H05

Published electronically:
May 8, 2006

MathSciNet review:
2231913

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a sequence of positive real numbers. We define as the space of functions which are analytic in the unit disc , continuous on and such that

**1.**Aharon Atzmon,*Boundary values of absolutely convergent Taylor series*, Ann. of Math. (2)**111**(1980), no. 2, 231–237. MR**569071**, 10.2307/1971199**2.**Lennart Carleson,*Sets of uniqueness for functions regular in the unit circle*, Acta Math.**87**(1952), 325–345. MR**0050011****3.**Jean-Pierre Kahane and Raphaël Salem,*Ensembles parfaits et séries trigonométriques*, Actualités Sci. Indust., No. 1301, Hermann, Paris, 1963 (French). MR**0160065****4.**B. I. Korenblyum,*Closed ideals in the ring*, J. Func. Anal. Appl.**6**(1972), 203-214.**5.**V. S. Korolevič,*A certain theorem of Beurling and Carleson*, Ukrain. Mat. Ž.**22**(1970), 823–828 (Russian). MR**0289785****6.**B. A. Taylor and D. L. Williams,*Ideals in rings of analytic functions with smooth boundary values*, Canad. J. Math.**22**(1970), 1266–1283. MR**0273024****7.**B. A. Taylor and D. L. Williams,*Boundary zero sets of 𝐴^{∞} functions satisfying growth conditions*, Proc. Amer. Math. Soc.**35**(1972), 155–160. MR**0310253**, 10.1090/S0002-9939-1972-0310253-9

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Additional Information

**Cyril Agrafeuil**

Affiliation:
LaBAG, CNRS-UMR 5467, Université Bordeaux I, 351 cours de la Libération, 33451 Talence, France

Address at time of publication:
LATP, Faculté des Sciences de Saint-Jérôme, Bâtiment Henri Poincaré, Cour A, 13397 Marseille cedex 20, France

Email:
Cyril.Agrafeuil@math.u-bordeaux.fr

DOI:
http://dx.doi.org/10.1090/S0002-9939-06-08399-7

Keywords:
Boundary zero of analytic functions,
sets of uniqueness,
spaces of analytic functions,
Beurling-Carleson sets

Received by editor(s):
September 23, 2004

Received by editor(s) in revised form:
May 26, 2005

Published electronically:
May 8, 2006

Communicated by:
David R. Larson

Article copyright:
© Copyright 2006
American Mathematical Society