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Extensions of a theorem of Marcinkiewicz-Zygmund and of Rogosinski's formula and an application to Universal Taylor series
Author(s):
E.
S.
Katsoprinakis;
M.
Papadimitrakis
Journal:
Proc. Amer. Math. Soc.
127
(1999),
2083-2090.
MSC (1991):
Primary 30B30;
Secondary 41A58, 42A24, 30E10
Posted:
March 16, 1999
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Abstract:
This paper extends Rogosinski's formula and the Marcinkiewicz-Zygmund Theorem about circular structure of the limit points of the partial sums of (C,1) summable Taylor series. Also a result about summability of  Taylor series is proved and an application on Universal Taylor series is given.
References:
- 1.
- Hardy, G. H., Divergent Series, Oxford University Press, 1967. MR 93g:01100 (1992 reprint)
- 2.
- Kahane, J. -P., Sur la structure circulaire des ensembles de points limites des sommes partielles d'une serie de Taylor, Acta Sci. Math. (Szeged) 45, 1-4 (1983) 247-251. MR 85f:30003
- 3.
- Kahane, J. -P., Baire Theory in Fourier and Taylor series, Conference in the honor of Donald Newman, Philadelphia, March 1996.
- 4.
- Kahane, J. -P., General Properties of Taylor series 1896-1996, L'Escurial, Spain, June 1996. CMP 98:09
- 5.
- Marcinkiewicz, J. and A. Zygmund, On the behavior of trigonometric series and power series, Trans. Amer. Math. Soc. 50 (1941) 407-453. MR 3:105d
- 6.
- Melas, A., V. Nestoridis and I. Papadoperakis, Growth of coefficients of universal Taylor series and comparison of two classes of functions, Journal d'Analyse Mathematique 73 (1997) 187-202. CMP 98:10
- 7.
- Nestoridis, V., Universal Taylor Series, Ann. Inst. Fourier, Grenoble 46 5 (1996) 1293-1306. MR 97k:30001
- 8.
- Nestoridis, V. and S. K. Pichorides, The circular structure of the set of the limit points of partial sums of Taylor series, Seminaire d'Analyse Harmonique, Univ. de Paris-Sud, Mathematiques, Orsay, France (1989-90) 71-77.
- 9.
- Zygmund, A., Trigonometric Series, second edition reprinted Vol. I, II, Cambridge University Press, 1979. MR 58:29731
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Additional Information:
E.
S.
Katsoprinakis
Affiliation:
Department of Mathematics, University of Crete, 714 09 Heraklion - Crete, Greece
Email:
katsopr@talos.cc.uch.gr
M.
Papadimitrakis
Affiliation:
Department of Mathematics, University of Crete, 714 09 Heraklion - Crete, Greece
Email:
papadim@talos.cc.uch.gr
DOI:
10.1090/S0002-9939-99-05150-3
PII:
S 0002-9939(99)05150-3
Received by editor(s):
October 13, 1997
Posted:
March 16, 1999
Communicated by:
Albert Baernstein II
Copyright of article:
Copyright
1999,
American Mathematical Society
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