Comptes Rendus
Analyse et géométrie complexes
Universal radial limits of meromorphic functions in the unit disk
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 893-898.

We consider the space of meromorphic functions in the unit disk 𝔻 and show that there exists a dense G δ -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.

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DOI : 10.5802/crmath.352
Classification : 30K15, 30D40, 30D35, 30D30
Thierry Meyrath 1

1 University of Luxembourg, Department of Mathematics, 6, avenue de la Fonte, 4364 Esch-sur-Alzette, Luxembourg
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {Universal radial limits of meromorphic functions in the unit disk},
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     doi = {10.5802/crmath.352},
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Thierry Meyrath. Universal radial limits of meromorphic functions in the unit disk. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 893-898. doi : 10.5802/crmath.352. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.352/

[1] Frédéric Bayart Universal radial limits of holomorphic functions, Glasg. Math. J., Volume 47 (2005) no. 2, pp. 261-267 | Zbl

[2] Luis Bernal-González; Maria C. Calderón-Moreno; Jose A. Prado-Bassas Maximal cluster sets along arbitrary curves, J. Approx. Theory, Volume 129 (2004) no. 2, pp. 207-216

[3] Luis Bernal-González; Maria C. Calderón-Moreno; Jose A. Prado-Bassas Simultaneously maximal radial cluster sets, J. Approx. Theory, Volume 135 (2005) no. 1, pp. 114-124

[4] Stéphane Charpentier Holomorphic functions with universal boundary behaviour, J. Approx. Theory, Volume 254 (2020), 105391, 19 pages

[5] Stéphane Charpentier; Vassili Nestoridis On the boundary behaviour of derivatives of functions in the disc algebra, C. R. Acad. Sci. Paris, Volume 356 (2018) no. 7, pp. 732-736 | Zbl

[6] Edward F. Collingwood; Mary L. Cartwright Boundary theorems for a function meromorphic in the unit circle, Acta Math. (1952) no. 57, pp. 86-146

[7] John B. Conway Functions of one complex variable I, Graduate Texts in Mathematics, 11, Springer, 1978

[8] Yves Dupain Extension à la dimension n d’un théorème de Ortel et Schneider, Math. Z., Volume 206 (1991) no. 1, pp. 71-80

[9] Paul M. Gauthier; Alice Roth; Joseph L. Walsh Possibility of uniform rational approximation in the spherical metric, Can. J. Math., Volume 28 (1976), pp. 112-115

[10] Walter K. Hayman Meromorphic functions, Oxford Mathematical Monographs, Clarendon Press, 1964

[11] Stanislaw Kierst; Edward Szpilrajn Sur certaines singularités des fonctions analytiques uniformes, Fundam. Math., Volume 21 (1933), pp. 276-294

[12] Gerald R. MacLane Meromorphic functions with small characteristic and no asymptotic values, Mich. Math. J., Volume 8 (1961), pp. 177-185

[13] Thierry Meyrath Compositionally universal meromorphic functions, Complex Var. Elliptic Equ., Volume 64 (2019) no. 9, pp. 1534-1545

[14] Kiyoshi Noshiro Contributions to the theory of meromorphic functions in the unit circle, J. Fac. Sci., Hokkaido Univ., Ser. I, Volume 7 (1939), pp. 149-159

[15] Lawrence Zalcman Analytic capacity and rational approximation, Lecture Notes in Mathematics, 50, Springer, 1968

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