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

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

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.**A. Atzmon,*Boundary values of absolutely convergent Taylor series*, Annals of Math.**111**(1980), 231-237. MR**0569071 (81j:30008)****2.**L. Carleson,*Sets of uniqueness for functions regular in the unit circle*, Acta. Math.**87**(1952), 325-345. MR**0050011 (14:261a)****3.**J. P. Kahane, R. Salem,*``Ensembles parfaits et séries trigonométriques''*, Paris, Hermann, 1963. MR**0160065 (28:3279)****4.**B. I. Korenblyum,*Closed ideals in the ring*, J. Func. Anal. Appl.**6**(1972), 203-214.**5.**V. S. Korolevich,*On a theorem of Beurling and Carleson*, Ukr. Math. J.**22**(1970), 710-714 (1971). MR**0289785 (44:6972)****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 (42:7905)****7.**B. A. Taylor and D. L. Williams,*Boundary zero sets of functions satisfying growth conditions*, Proc. of Amer. Math. Soc. (1)**35**(1972), 155-160. MR**0310253 (46:9354)**

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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:
https://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