Universal Faber and Taylor series on an unbounded domain of infinite connectivity

References

• Pal , J . 1914 . Zwei Kleine Bemerkungen . Tohoku Math. J. , 6 : 42 – 43 .
   Google Scholar
• Seleznev , AI . 1951 . On universal power series . Math. Sb. , 28 : 453 – 460 . (in Russian)
   Google Scholar
• Luh , W . 1970 . Approximation analytischer functionen durch überkonvergente potenzreihen und deren matrix-transformierten . Mitt. Math. Sem. Giessen , 88 : 1 – 56 .
   Google Scholar
• Chui , CK and Parnes , MN . 1971 . Approximation by overconvergence of power series . J. Math. Anal. Appl. , 36 : 693 – 696 .
   Web of Science ®Google Scholar
• Nestoridis , V . 1996 . Universal Taylor series . Ann. Inst. Fourier , 46 : 1293 – 1306 .
   Web of Science ®Google Scholar
• Nestoridis , V . 2003 . A strong notion of universal Taylor series . J. London Math. Soc. , 68 : 712 – 724 .
   Web of Science ®Google Scholar
• Katsoprinakis , E , Nestoridis , V and Papadoperakis , I . 2001 . Universal Faber series . Analysis (Munich) , 21 : 339 – 363 .
   Google Scholar
• Mayenberger , D and Müller , J . 2005 . Faber series with Ostrowski gaps . Complex Var. Theor. Appl. , 50 : 79 – 88 .
   Google Scholar
• Gehlen , W , Luh , W and Müller , J . 2000 . On the existence of O-universal functions . Complex Var. , 41 : 81 – 90 .
   Google Scholar
• Bacharoglou , A . 2009 . Universal Taylor series on doubly connected domains . Result. Math. , 53 : 9 – 18 .
   Web of Science ®Google Scholar
• Costakis , G . 2000 . Some remarks on universal functions and Taylor series . Math. Proc. Cambridge – Philos. Soc. , 128 : 157 – 175 .
   Web of Science ®Google Scholar
• Melas , A . 2001 . Universal functions on nonsimply connected domains . Ann. Inst. Fourier , 51 : 1539 – 1551 .
   Web of Science ®Google Scholar
• Tsirivas , N . 2006 . Boundedness, regularity and smoothness of universal Taylor series . Arch. Math. , 87 : 427 – 435 .
   Google Scholar
• Vlachou , V . 2002 . A universal Taylor series in the doubly connected domain ℂ ∖ {1} . Complex Var. Theor. Appl. , 47 : 123 – 129 .
   Google Scholar
• Grosse-Erdmann , K-G . 1999 . Universal families and hypercyclic operators . Bull. Amer. Math. Soc. , 36 : 345 – 381 .
   Web of Science ®Google Scholar
• Kahane , JP . 2000 . Baire's category theorem and trigonometric series . J. Anal. Math. , 80 : 143 – 182 .
   Web of Science ®Google Scholar
• Costakis , G and Vlachou , V . 2006 . Universal Taylor series on non-simply connected domains . Analysis , 26 : 347 – 363 .
   Google Scholar
• Markushevich , AJ . 1985 . Theory of Functions of a Complex Variable , New York : Chelsea Publishing Company .
   Google Scholar
• Grosse-Erdmann , K-G . 1987 . Holomorphe monster und universelle functionen . Mitt. Math. Sem. Giessen , 176
   Google Scholar
• Burckel , RB . 1979 . An introduction to Classical Complex Analysis , Basel : Birkhäuser Verlag .
   Google Scholar
• Bayart , F , Grosse-Erdmann , K-G , Nestoridis , V and Papadimitropoulos , Ch . 2008 . Abstract theory of universal series and applications . Proc. London Math. Soc. , 96 ( 2 ) : 417 – 463 .
   Google Scholar
• Bernal-Gonzalez , L . 1999 . Densely hereditarily hypercyclic sequences and large hypercyclic manifolds . Proc. Amer. Math. Soc. , 127 : 3279 – 3285 .
   Web of Science ®Google Scholar
• Bayart , F . 2005 . Universal Taylor series on general doubly connected domains . Bull. London Math. Soc , 37 : 878 – 884 .
   Web of Science ®Google Scholar
• Costakis , G . 2005 . Universal Taylor series on doubly connected domains in respect to every center . J. Approx.Theory , 134 : 1 – 10 .
   Web of Science ®Google Scholar
• Stephen J. Gardiner, C.R. Nikolaos Tsirivas, Acad. Sci. Paris, Ser. I 348 (2010), pp. 521–524.
   Google Scholar
• V. Nestoridis, C. Papachristodoulos, Universal Taylor series on arbitrary planar domains, C.R. Math. Acad. Sci. Paris 347 (7–8) (2009), pp. 363–367.
   Google Scholar
• Vlachou , V . 2007 . “ Universal Taylor series on a non-simply connected domain and Hadamard-Ostrowski gaps ” . In Complex and Harmonic Analysis , 221 – 229 . Lancaster, PA : Destech Publ., Inc. .
   Google Scholar