no. G8
Analyse et géométrie complexes
Universal radial limits of meromorphic functions in the unit disk
Meyrath, Thierry1
1 University of Luxembourg, Department of Mathematics, 6, avenue de la Fonte, 4364 Esch-sur-Alzette, Luxembourg
Comptes Rendus. Mathématique, Tome 360 (2022) no. G8, 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.

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

1 University of Luxembourg, Department of Mathematics, 6, avenue de la Fonte, 4364 Esch-sur-Alzette, Luxembourg 
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Meyrath, Thierry. Universal radial limits of meromorphic functions in the unit disk. Comptes Rendus. Mathématique, Tome 360 (2022) no. G8, pp. 893-898. doi : 10.5802/crmath.352. http://archive.numdam.org/articles/10.5802/crmath.352/

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

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

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

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

[5] Charpentier, Stéphane; Nestoridis, Vassili 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 | DOI | MR | Zbl

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

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

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

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

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

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

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

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

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

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