Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Boundary spectra of uniform Frostman Blaschke products


Author: Alec Matheson
Journal: Proc. Amer. Math. Soc. 135 (2007), 1335-1341
MSC (2000): Primary 30D50, 30D40
DOI: https://doi.org/10.1090/S0002-9939-06-08470-X
Published electronically: November 29, 2006
MathSciNet review: 2276642
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A closed set $ F$ in the unit circle $ \mathbb{T}$ is the boundary spectrum of a uniform Frostman Blaschke product if and only if $ F$ is nowhere dense in $ \mathbb{T}$.


References [Enhancements On Off] (What's this?)

  • 1. Joseph A. Cima, Alec L. Matheson, and William T. Ross, The Cauchy transform, Mathematical Surveys and Monographs, vol. 125, American Mathematical Society, Providence, RI, 2006.
  • 2. E. F. Collingwood and A. J. Lohwater, The theory of cluster sets, Cambridge Tracts in Mathematics and Mathematical Physics, No. 56, Cambridge University Press, Cambridge, 1966. MR 0231999 (38:325)
  • 3. Otto Frostman, Sur les produits de Blaschke, Kungl. Fysiografiska Sällskapets i Lund Förhandlingar [Proc. Roy. Physiog. Soc. Lund] 12 (1942), no. 15, 169-182. MR 0012127 (6:262e)
  • 4. John B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol. 96, Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York, 1981. MR 628971 (83g:30037)
  • 5. S. V. Hrušcev and S. A. Vinogradov, Inner functions and multipliers of Cauchy type integrals, Ark. Mat. 19 (1981), no. 1, 23-42. MR 625535 (83c:30027)
  • 6. Pertti Mattila, Geometry of sets and measures in Euclidean spaces, Cambridge Studies in Advanced Mathematics, vol. 44, Cambridge University Press, Cambridge, 1995. MR 1333890 (96h:28006)
  • 7. P. J. McKenna, Discrete Carleson measures and some interpolation problems, Michigan Math. J. 24 (1977), no. 3, 311-319. MR 0481016 (58:1163)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 30D50, 30D40

Retrieve articles in all journals with MSC (2000): 30D50, 30D40


Additional Information

Alec Matheson
Affiliation: Department of Mathematics, Lamar University, P.O. Box 10047, Beaumont, Texas 77710
Email: matheson@math.lamar.edu

DOI: https://doi.org/10.1090/S0002-9939-06-08470-X
Received by editor(s): June 30, 2005
Received by editor(s) in revised form: August 10, 2005
Published electronically: November 29, 2006
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society