Logarithmic means and summability by the circle methods
HTML articles powered by AMS MathViewer
- by M. R. Parameswaran PDF
- Proc. Amer. Math. Soc. 52 (1975), 279-282 Request permission
Abstract:
It is proved that if the logarithmic means of a sequence $\{ {s_n}\}$ satisfy a certain order condition then the sequence $\{ {s_n}\}$ will be summable by every circle method (Kreisverfahren) stronger than convergence; the condition is shown to be a best possible one, for even summability by the collective circle method. A second set of conditions leading to the conclusion of summability by every circle method is also proved.References
- G. H. Hardy, Divergent Series, Oxford, at the Clarendon Press, 1949. MR 0030620
- G. G. Lorentz, Direct theorems on methods of summability, Canad. J. Math. 1 (1949), 305–319. MR 32023, DOI 10.4153/cjm-1949-028-6
- W. Meyer-König, Untersuchungen über einige verwandte Limitierungsverfahren, Math. Z. 52 (1949), 257–304 (German). MR 32021, DOI 10.1007/BF02230694
- M. R. Parameswaran, On summability functions for the circle family of methods, Proc. Nat. Inst. Sci. India Part A 25 (1959), 171–175. MR 107767
- K. Zeller and W. Beekmann, Theorie der Limitierungsverfahren, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 15, Springer-Verlag, Berlin-New York, 1970 (German). Zweite, erweiterte und verbesserte Auflage. MR 0264267
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 52 (1975), 279-282
- MSC: Primary 40G10
- DOI: https://doi.org/10.1090/S0002-9939-1975-0387883-4
- MathSciNet review: 0387883