Thumbnail
Access Restriction
Open

Source CiteSeerX
Content type Text
File Format PDF
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Series F ♦ Full Measure ♦ Ipin2x N ♦ Intrinsic Descrip-tion ♦ Intermediate Step
Abstract Abstract. For any s ∈ (1/2, 1], the series Fs(x) = n=1 e ipin2x/ns converges almost everywhere on [−1, 1] by a result of Hardy-Littlewood concerning the growth of the sums∑N n=1 e ipin2x, but not everywhere. However, there does not yet exist an intrinsic descrip-tion of the set of convergence for Fs. In this paper, we define in terms of even continued fractions a subset of points of [−1, 1] of full measure where the series converges. As an intermediate step, we prove that, for s> 0, the sequence of functions N∑ n=1 eipin
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Learning Resource Type Article