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A Karamata Method I. Elementary Properties and Applications

Published online by Cambridge University Press:  20 November 2018

Mirosław Baran
Mirosław Baran*
Affiliation:
Department of Mathematics Pedagogical University of Cracow 30-084 Cracow, Podchorazych 2 Poland
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Abstract

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In this paper we present a new approach to classical Karamata's results concerning the Hardy-Littlewood tauberian theorem.

Keywords

40E0510K20.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 2 , 01 June 1991 , pp. 147 - 157
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Erdös, P., On the distribution of additive functions, Ann. of Math. 47(1946), 1–20.Google Scholar
2. Hardy, G. H., Little wood, J. E., Tauberian theorems concerning power series and Dirichlets series whose coefficients are positive, Proc. London Math. Soc. Ser. 2(1914), 13, 174–191.Google Scholar
3. Kalecki, M., On the sum Σn≦x {f(x/n)}, Commentationes Math., 11(1968), 2, 183–191.Google Scholar
4. Karamata, J., Uberdie Hardy-Littlewoodschen Umkehrungendes Abelschen Stetigkeitsatzes, Math. Zeitschrift, 32(1930), 319–320.Google Scholar
5. Kuczma, M. E., An Introduction to the Theory of Functional Equations and Inequalities, Polish Scientific Publishers, Warsaw, 1985.Google Scholar
6. Mercier, A., Comportementasymptotique de Σ Pa{x/p}k , Canad. Math. Bull., (3), 30(1987), 309–317.Google Scholar
7. Mercier, A., Nowak, G., On the asymptotic behaviour of sums Σ g(n){x/ n}k , Mh. Math., 99(1985), 213— 221.Google Scholar
8. Titchmarsch, E. C., The theory of functions, 2nd éd., Oxford University Press, 1978.Google Scholar
9. Titchmarsch, E. C., The theory of the Riemann zeta function, Oxford University Press, 1951.Google Scholar