Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-24T12:23:12.412Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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