Abstract
For certain non-simply connected domains of even infinite connectivity, we prove that there exist holomorphic functions such that a) their Faber expansions with respect to suitable compact sets Γ have approximating properties outside their domain of holomorphy, and b) the coefficients of the Faber expansions have the property of Hadamard-Ostrowski gaps.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
F. Bayart, Universal Taylor series on general doubly connected domains, Bull. London Math. Soc. 37 (2005), 878–884.
F. Bayart, K-G. Grosse-Erdmann, V. Nestoridis and C. Papadimitropoulos, Abstract theory of universal series and applications, Proc. London Math. Soc. 96 (2008), 417–463.
F. Bayart and V. Nestoridis, Universal Taylor series have a strong form of universality, J. Anal. Math 104 (2008), 69–82.
L. Bernal-Gonzales, Densely hereditary hypercyclic sequences and large hypercyclic manifolds, Proc. Amer. Math. Soc. 127, 3279–3285.
R. B. Burkel, An Introduction to Classical Complex Analysis, Birkhäuser Verlag, Basel, 1979.
G. Costakis, Some remarks on universal functions and Taylor series, Math. Proc. Cambridge Philos. Soc. 128 (2000), 157–175.
G. Costakis, Universal Taylor series on doubly connected domains with respect to every center, J. Approx. Theory 134 (2005), 1–10.
G. Costakis and V. Vlachou, Universal Taylor series on non-simply connected domains, Analysis 26 (2006), 347–363.
W. Gehlen, Overconvergent power series and conformal maps, J. Math. Anal. Appl.198 (1996), 490–505.
K. G. Grosse-Erdmann, Holomorphe Monster und universelle Funktionen, Mitt. Math. Sem. Giessen 176 (1987), 1–84.
E. Katsoprinakis, V. Nestoridis and I. Papadoperakis, Universal Faber series, Analysis 21 (2001), 339–363.
A. J. Markushevich, Theory of Functions of a Complex Variable, Vol. III, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967, xi+360 pp.
D. Mayenberger and J. Müller, Faber series with Ostrowski gaps, Complex Var. Theory Appl. 50 (2005), 79–88.
A. Melas, Universal functions on non-simply connected domains, Ann. Inst. Fourier (Grenoble) 51 (2001), 1539–1551.
V. Nestoridis, Universal Taylor series, Ann. Inst. Fourier (Grenoble) 46 (1996), 1293–1306.
A. Ostrowski, Über eine Eigenschaft gewisser Potenzreihen mit unendlich vielen verschwindenden Koeffizienten, Sitz.ber. Preuss. Akad. Wiss. (Berlin) Phys.-Math. Kl. (1921), 557–565.
—, Uber Potenzreihen, die überkonvergente Abschnittsfolgen besitzen, Sitz.ber. Preuss. Akad. Wiss. (Berlin) Phys.-Math. Kl. (1923), 185–192.
W. Rudin, Real and Complex Analysis, 3rd edn McGraw-Hill, 1966.
N. Tsirivas, Universal Faber and Taylor series on an unbounded domain of infinite connectivity, submitted.
V. Vlachou, A universal Taylor series in the doubly connected domain C 1, Complex Variables 47 (2002), 123–129.
V. Vlachou, Universal Taylor series on a non-simply connected domain and Hadamard-Ostrowski gaps, in: Complex and Harmonic Analysis, DEStech Publ. Inc. Lancaster, PA, 2007, 221–229.
V. Vlachou, Functions with universal Faber expansions, J. London Math. Soc. 80 (2009), 531–543.
Author information
Authors and Affiliations
Additional information
This work has been partially supported by the Caratheodory research program (C164). During this research the first author was supported by the State Scholarships Foundation of Greece (I.K.Y.).
Rights and permissions
About this article
Cite this article
Tsirivas, N., Vlachou, V. Universal Faber Series with Hadamard-Ostrowski Gaps. Comput. Methods Funct. Theory 10, 155–165 (2010). https://doi.org/10.1007/BF03321760
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03321760