Skip to main content
Log in

On a boundary property of Blaschke products

  • Published:
Analysis Mathematica Aims and scope Submit manuscript

Abstract

A Blaschke product has no radial limits on a subset E of the unit circle T but has unrestricted limit at each point of T \ E if and only if E is a closed set of measure zero.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R. D. Berman, The sets of fixed radial limit value for inner functions, Illinois J. Math. (2), 29 (1985), 191–219.

    MathSciNet  MATH  Google Scholar 

  2. E. F. Collingwood, On sets of maximum indetermination of analytic functions, Math. Z., 67 (1957), 377–396.

    Article  MathSciNet  MATH  Google Scholar 

  3. E. F. Collingwood, On a theorem of Eggleston concerning cluster sets, J. London Math. Soc., 30, (1955), 425–428.

    Article  MathSciNet  MATH  Google Scholar 

  4. E. F. Collingwood and A. J. Lohwater, The Theory of Cluster Sets, Cambridge University Press (Cambridge, 1966).

    Book  MATH  Google Scholar 

  5. A. A. Danielyan, A theorem of Lohwater and Piranian, Proc. Amer. Math. Soc., 144 (2016), 3919–3920.

    Article  MathSciNet  MATH  Google Scholar 

  6. A. A. Danielyan, On Fatou’s theorem, Anal. Math. Phys., 10 (2020), Article no. 28, 4 pp.

    Article  MathSciNet  MATH  Google Scholar 

  7. H. G. Eggleston, A property of bounded analytic functions, Comment. Math. Helv., 30 (1956), 139–143.

    Article  MathSciNet  Google Scholar 

  8. K. Hoffman, Banach Spaces of Analytic Functions, Prentice Hall (Englewood Cliffs, NJ, 1962).

    MATH  Google Scholar 

  9. A. J. Lohwater and G. Piranian, The boundary behavior of functions analytic in a disk, Ann. Acad. Sci. Fenn. Ser. A/I. (1957), no. 239, 17 pp.

    MathSciNet  MATH  Google Scholar 

  10. A. Nicolau, Blaschke product with prescribed radial limits, Bull. London Math. Soc., 23 (1991), 249–255.

    Article  MathSciNet  MATH  Google Scholar 

  11. K. Noshiro, Cluster Sets, Springer-Verlag (Berlin, 1960).

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. A. Danielyan.

Additional information

The first author was supported by Simons Foundation (Grant No. 430329).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Danielyan, A.A., Pasias, S. On a boundary property of Blaschke products. Anal Math 49, 403–408 (2023). https://doi.org/10.1007/s10476-023-0212-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10476-023-0212-8

Key words and phrases

Mathematics Subject Classification

Navigation