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.
Similar content being viewed by others
References
R. D. Berman, The sets of fixed radial limit value for inner functions, Illinois J. Math. (2), 29 (1985), 191–219.
E. F. Collingwood, On sets of maximum indetermination of analytic functions, Math. Z., 67 (1957), 377–396.
E. F. Collingwood, On a theorem of Eggleston concerning cluster sets, J. London Math. Soc., 30, (1955), 425–428.
E. F. Collingwood and A. J. Lohwater, The Theory of Cluster Sets, Cambridge University Press (Cambridge, 1966).
A. A. Danielyan, A theorem of Lohwater and Piranian, Proc. Amer. Math. Soc., 144 (2016), 3919–3920.
A. A. Danielyan, On Fatou’s theorem, Anal. Math. Phys., 10 (2020), Article no. 28, 4 pp.
H. G. Eggleston, A property of bounded analytic functions, Comment. Math. Helv., 30 (1956), 139–143.
K. Hoffman, Banach Spaces of Analytic Functions, Prentice Hall (Englewood Cliffs, NJ, 1962).
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.
A. Nicolau, Blaschke product with prescribed radial limits, Bull. London Math. Soc., 23 (1991), 249–255.
K. Noshiro, Cluster Sets, Springer-Verlag (Berlin, 1960).
Author information
Authors and Affiliations
Corresponding author
Additional information
The first author was supported by Simons Foundation (Grant No. 430329).
Rights and permissions
About this article
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
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10476-023-0212-8