Home > Articles > Published articles > Vitali's theorem without uniform boundedness |
Date: | 2016 |
Abstract: | Let {fm}m≥1 be a sequence of holomorphic functions defined on a bounded domain D ⊂ Cn or a sequence of rational functions (1 ≤ deg rm ≤ m) defined on Cn. We are interested infinding sufficient conditions to ensure the convergence of {fm}m≥1 on a large set provided the convergence holds pointwise on a not too small set. This type of result is inspired from a theorem of Vitali which gives a positive answer for uniformly bounded sequence. |
Rights: | Tots els drets reservats. |
Language: | Anglès |
Document: | Article ; recerca ; Versió publicada |
Subject: | Rapid convergence ; Convergence in capacity ; Pluripolar set ; Relative capacity |
Published in: | Publicacions matemàtiques, Vol. 60 Núm. 2 (2016) , p. 311-334 (Articles) , ISSN 2014-4350 |
24 p, 419.8 KB |