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Fatou-Riesz-theorems in general sequence spaces

Published online by Cambridge University Press:  20 January 2009

Gerhard Otto Müller  and
Rolf Trautner
Gerhard Otto Müller
Affiliation:
Universität UlmAbteilung Für Mathematik VD-7900 Ulm, West Germany
Rolf Trautner
Affiliation:
Universität UlmAbteilung Für Mathematik VD-7900 Ulm, West Germany
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Consider a formal series with partial sums and the corresponding power series . Throughout we will assume that f is analytic for |z| <1, i.e. that A classical theorem of Fatou-Riesz (see (1, 4)) states that if and

then is convergent to 0.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 23 , Issue 2 , June 1980 , pp. 199 - 205
Copyright
Copyright © Edinburgh Mathematical Society 1980

References

REFERENCES

(1)Fatou, P., Séries trigonométriques et séries de Taylor, Acta Math. 30 (1906), 335–400.Google Scholar
(2)Jurkat, W., Peyerimhoff, A., Der Satz von Fatou-Riesz und der Riemannsche Lokalisationssatz bei absoluter Konvergenz, Arch. Math. 4 (1953), 285–297.CrossRefGoogle Scholar
(3)Jurkat, W. and Peyerimhoff, A., Über einen absoluten Fatou-Rieszschen Satz für Laplaceintegrale, Acad. Serbe Sci. Publ. Inst. Math. 7 (1954), 61–68.Google Scholar
(4)Riesz, M., Über einen Satz des Herrn Fatou, J. reine angew. Math. 140 (1911), 89–99.Google Scholar