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On asymptotic behaviours of trigonometric series with δ-Quasi-monotone coefficients

Published online by Cambridge University Press:  20 January 2009

Ming-Chit Liu
Ming-Chit Liu
Affiliation:
Department of Mathematics, University of Hong Kong
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Let

The asymptotic behaviours of ƒ(x) and g(x), as x→+0, were first given by G. H. Hardy in (4), (5). In his papers {an}; is a monotone decreasing sequence. Further results on the asymptotic behaviours of ƒ(x) and g(x), as x→+0, for monotone coefficients have been given in (9) and (1). Recently, the results have been generalized to quasi-monotone coefficients.

This paper is concerned with asymptotic behaviours of ƒ(x) and g(x) for δ-quasi-monotone coefficients.

In what follows, we shall denote by L(x) a slowly varying function in the sense of Karamata (6), i.e.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 16 , Issue 4 , December 1969 , pp. 305 - 316
Copyright
Copyright © Edinburgh Mathematical Society 1969

References

REFERENCES

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