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Universal Taylor series and summability
- 作者:S. Charpentier (1)
A. Mouze (2) (3)
1. Laboratoire d鈥橝nalyse ; Topologie et Probabilit茅s ; UMR 7353 ; Aix-Marseille Universit茅 ; Technop么le Ch芒teau-Gombert ; 39 rue F. Joliot Curie ; 13453聽 ; Marseille Cedex 13 ; France 2. Laboratoire Paul Painlev茅 ; UMR 8524 ; Cit茅 Scientifique ; 59650聽 ; Villeneuve d鈥橝scq ; France 3. 脡cole Centrale de Lille ; Cit茅 Scientifique ; CS20048 ; 59651 ; Villeneuve d鈥橝scq Cedex ; France
- 关键词:Universal Taylor series ; Ostrowski ; gaps ; Matrix summability method ; 30K05 ; 40A05 ; 41A10 ; 47A16
- 刊名:Revista Matemática Complutense
- 出版年:2015
- 出版时间:January 2015
- 年:2015
- 卷:28
- 期:1
- 页码:153-167
- 全文大小:195 KB
- 参考文献:1. Bayart, F.: Boundary behavior and Ces脿ro means of universal Taylor series. Rev. Mat. Complut. 19(1), 235鈥?47 (2006) 209/rev_REMA.2006.v19.n1.16662" target="_blank" title="It opens in new window">CrossRef
2. Bayart, F., Grosse-Erdmann, K.-G., Nestoridis, V., Papadimitropoulos, C.: Abstract theory of universal series and applications. Proc. Lond. Math. Soc. 96, 417鈥?63 (2008) 2/plms/pdm043" target="_blank" title="It opens in new window">CrossRef 3. Bernal-Gonz谩lez, L., Bonilla, A., Calder贸n-Moreno, M.C., Prado-Bassas, J.A.: Universal Taylor series with maximal cluster sets. Rev. Mat. Iberoam. 25, 757鈥?80 (2009) 2" target="_blank" title="It opens in new window">CrossRef 4. Bernal-Gonz谩lez, L., Calder贸n-Moreno, M.C., Luh, W.: Universal matrix transforms of holomorphic functions. Houston J. Math. 32, 315鈥?24 (2006) 5. Bernal-Gonz谩lez, L., Pellegrino, D., Seoane-Sep煤lveda, J.B.: Linear subsets of nonlinear sets in topological vector spaces. Bull. Am. Math. Soc. 51, 71鈥?30 (2014) 273-0979-2013-01421-6" target="_blank" title="It opens in new window">CrossRef 6. Boos, J.: Classical and Modern Methods in Summability. Oxford University Press, Oxford (2000) 7. Charpentier, S.: On the closed subspaces of universal series in Banach and Fr茅chet spaces. Studia Math. 198, 121鈥?45 (2010) 2-2" target="_blank" title="It opens in new window">CrossRef 8. Charpentier, S., Mouze, A., Munnier, V.: Generalized universal series (submitted for publication) 9. Costakis, G.: Which maps preserve universal functions? In: Mathematisches Forschungsinstitut Oberwolfach, Report No 6/2008 (2008) 10. Gharibyan, T.L., Luh, W.: Summability of elongated sequences. Comput. Methods Funct. Theor. 11(1), 59鈥?0 (2011) 3321790" target="_blank" title="It opens in new window">CrossRef 11. Gehlen, W., Luh, W., M眉ller, J.: On the existence of O-universal functions. Complex Variables Theory Appl. 41(1), 81鈥?0 (2000) 30008815238" target="_blank" title="It opens in new window">CrossRef 12. Hardy, G.H.: Divergent Series. Oxford University Press, New York (1949) 13. Kahane, J.-P., Melas, A.: Restricted universality of power series. Bull. Lond. Math. Soc. 33, 543鈥?52 (2001) 2/S0024609301008384" target="_blank" title="It opens in new window">CrossRef 14. Katsoprinakis, E.S.: Coincidence of some classes of universal functions. Rev. Mat. Complut. 22(2), 427鈥?45 (2009) 209/rev_REMA.2009.v22.n2.16279" target="_blank" title="It opens in new window">CrossRef 15. Luh, W.: Approximation analytischer Funktionen durch 眉berkonvergente Potenzreihen und deren Matrix-Transformierten. Mitt. Math. sem. Giessen 88, 1鈥?6 (1970) 16. Melas, A., Nestoridis, V.: Universality of Taylor Series as a Generic Property of Holomorphic Functions. Adv. Math. 157, 138鈥?76 (2001) 2000.1955" target="_blank" title="It opens in new window">CrossRef 17. Melas, A., Nestoridis, V., Papadoperakis, I.: Growth of coefficients of universal Taylor series and comparison of two classes of functions. J. Anal. Math. 73, 187鈥?02 (1997) 2788143" target="_blank" title="It opens in new window">CrossRef 18. Menet, Q.: Sous-espaces ferm茅s de s茅ries universelles sur un espace de Fr茅chet. Studia Math. 207, 181鈥?95 (2011) 207-2-5" target="_blank" title="It opens in new window">CrossRef 19. Nestoridis, V.: Universal Taylor series. Ann. Inst. Fourier (Grenoble) 46(5), 1293鈥?306 (1996) 2/aif.1549" target="_blank" title="It opens in new window">CrossRef 20. Nestoridis, V.: An extension of the notion of universal Taylor series. Computational methods and function theory (1997) (Nicosia). Ser. Approx. Decompos., vol. 11, pp. 421鈥?30. World Sci. Publ., River Edge (1999) 21. Seleznev, A.I.: On universal power series. Math. Sbornik N.S. 28, 453鈥?60 (1951) 22. Wilansky, A.: Summability through functional analysis. Mathematics Studies, vol. 85. North-Holland, Amsterdam (1984) 23. Zygmund, A.: Trigonometric Series. Cambridge University Press, Cambridge (1979)
- 刊物类别:Mathematics and Statistics
- 刊物主题:Mathematics
Algebra Applications of Mathematics Geometry Mathematics Topology
- 出版者:Springer Milan
- ISSN:1988-2807
文摘
We introduce classes of universal Taylor series, both topologically and algebraically generic, whose image under some regular matrix summability methods are automatically universal.
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