Universal radial limits of meromorphic functions in the unit disk

[en] We consider the space of meromorphic functions in the unit disk $\D$ and show that there exists a dense $G_{\delta}$-subset of functions having universal radial limits. Our results complement known statements about holomorphic functions and further imply the existence of meromorphic functions having maximal cluster sets along certain subsets of $\D$.

Disciplines :

Mathematics

Author, co-author :

MEYRATH, Thierry ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit

External co-authors :

Language :

English

Title :

Universal radial limits of meromorphic functions in the unit disk

Publication date :

2022

Journal title :

Comptes Rendus. Mathématique

ISSN :

1631-073X

eISSN :

1778-3569

Publisher :

Elsevier Masson, Paris, France

Volume :

360

Pages :

893 - 898

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.352/

Available on ORBilu :

since 20 September 2022

Statistics

Number of views

51 (3 by Unilu)

Number of downloads

0 (0 by Unilu)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

WoS citations^™

publications

supporting

mentioning

contrasting

Smart Citations

Citing PublicationsSupportingMentioningContrasting

View Citations

See how this article has been cited at scite.ai

scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.

Bibliography

F. Bayart, "Universal radial limits of holomorphic functions", Glasg. Math. J. 47 (2005), no. 2, p. 261-267.
L. Bernal-González, M. C. Calderón-Moreno, J. A. Prado-Bassas, "Maximal cluster sets along arbitrary curves", J. Approx. Theory 129 (2004), no. 2, p. 207-216.
L. Bernal-González, M. C. Calderón-Moreno, J. A. Prado-Bassas, "Simultaneously maximal radial cluster sets", J. Approx. Theory 135 (2005), no. 1, p. 114-124.
S. Charpentier, "Holomorphic functions with universal boundary behaviour", J. Approx. Theory 254 (2020), article no. 105391 (19 pages).
S. Charpentier, V. Nestoridis, "On the boundary behaviour of derivatives of functions in the disc algebra", C. R. Acad. Sci. Paris 356 (2018), no. 7, p. 732-736.
E. F. Collingwood, M. L. Cartwright, "Boundary theorems for a function meromorphic in the unit circle", Acta Math. (1952), no. 57, p. 86-146.
J. B. Conway, Functions of one complex variable I, Graduate Texts in Mathematics, vol. 11, Springer, 1978.
Y. Dupain, "Extension à la dimension n d'un théorème de Ortel et Schneider", Math. Z. 206 (1991), no. 1, p. 71-80.
P. M. Gauthier, A. Roth, J. L. Walsh, "Possibility of uniform rational approximation in the spherical metric", Can. J. Math. 28 (1976), p. 112-115.
W. K. Hayman, Meromorphic functions, Oxford Mathematical Monographs, Clarendon Press, 1964.
S. Kierst, E. Szpilrajn, "Sur certaines singularités des fonctions analytiques uniformes", Fundam. Math. 21 (1933), p. 276-294.
G. R. MacLane, "Meromorphic functions with small characteristic and no asymptotic values", Mich. Math. J. 8 (1961), p. 177-185.
T. Meyrath, "Compositionally universal meromorphic functions", Complex Var. Elliptic Equ. 64 (2019), no. 9, p. 1534-1545.
K. Noshiro, "Contributions to the theory of meromorphic functions in the unit circle", J. Fac. Sci., Hokkaido Univ., Ser. I 7 (1939), p. 149-159.
L. Zalcman, Analytic capacity and rational approximation, Lecture Notes in Mathematics, vol. 50, Springer, 1968.

Similar publications

Sorry the service is unavailable at the moment. Please try again later.