A Positive Functional Bound for Certain Sine Sums

Author: Koumandos S.

Source: Analysis Mathematica, Volume 26, Number 1, 2000 , pp. 35-52(18)

Publisher: Springer

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Abstract:

The positivity of the sine sums $$\sum\limits_{k=1}^n {{{\sin k\theta } \over {k+1}}}$$> in (0, ) has been established by G. Brown and D. C. Wilson. In this paper, we sharpen this result by giving a positive functional estimate from below for these sine sums which does not depend on n. The corresponding problem for a more general class of sine sums is also discussed.

Language: English

Document Type: Regular paper

Affiliations: 1: Department of Mathematics and Statistics The University of Cyprus P.O. Box 20537, 1678 Nicosia Cyprus e-mail: skoumand@pythagoras.mas.ucy.ac.cy

Publication date: 2000-01-01