Zeros of analytic functions with infinitely differentiable boundary values

Author:
James G. Caughran

Journal:
Proc. Amer. Math. Soc. **24** (1970), 700-704

MSC:
Primary 30.67

DOI:
https://doi.org/10.1090/S0002-9939-1970-0252649-8

MathSciNet review:
0252649

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Abstract | References | Similar Articles | Additional Information

Abstract: A necessary and sufficient condition is proved that a set of points in the unit disk be the set of zeros of an analytic function with infinitely differentiable boundary values for every choice of

**[1]**A. Beurling,*Ensembles exceptionnels*, Acta Math.**72**(1939), 1-13. MR**1**, 226. MR**0001370 (1:226a)****[2]**L. Carleson,*Sets of uniqueness for functions regular in the unit circle*, Acta Math.**87**(1952), 325-345. MR**14**, 261. MR**0050011 (14:261a)****[3]**-,*A representation formula for the Dirichlet integral*, Math. Z.**73**(1960), 190-196. MR**22**#3803. MR**0112958 (22:3803)****[4]**J. G. Caughran,*Two results concerning the zeros of functions with finite Dirichlet integral*, Canad. J. Math.**21**(1969), 312-316. MR**0236396 (38:4692)****[5]**W. P. Novinger,*Holomorphic functions with infinitely differentiable boundary values*, (to appear). MR**0269861 (42:4754)****[6]**B. A. Taylor and D. L. Williams,*Ideals in rings of analytic functions with smooth boundary values*, (to appear). MR**0273024 (42:7905)****[7]**S. Warschawski,*Über einen Satz von O. D. Kellogg*, Gött. Nach. (1932), 73-86.**[8]**J. H. Wells,*On the zeros of functions with derivatives in**and*, Canad. J. Math, (to appear).

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1970-0252649-8

Keywords:
Bounded analytic function,
zero set,
boundary zeros,
domain with smooth boundary,
Carleson set,
Blaschke product

Article copyright:
© Copyright 1970
American Mathematical Society