On the divergence of a certain series

[摘要] We investigate for which real numbers alpha the series (4) converges, and prove that, even though it converges almost everywhere in the sense of Lebesgue to a periodic, with a period 1, odd function in L-2([0, 1]), it is divergent at uncountably many points, the set of which is dense in [0, 1]. Finally, we find the Fourier expansion of the function defined by the series (4). (c) 2005 Elsevier Inc. All rights reserved.

[发布日期] 2006-12-01

[关键词] uniform distribution;discrepancy;continued fractions;Ostrowski expansion