ID 6754
File
Authors
Keywords
non-differentiable
exponential sums
M¨obius function
Abstract
Fröberg [2] said that he believes f(x) = ∑∞ n=1 μ(n) / n einx being non-differentiable everywhere by computer computation, where i = √−1 and μ(n) is the Möbius function. In this paper, we show in Theorem 1.1 that for any interval in [0, 2π] there exists a positive Lebesgue measurable (L1-measurable) set such that f'(x) is not L2-measurable on its interval.
Publisher
鳥取大学教育支援・国際交流推進機構教育センター
Content Type
Departmental Bulletin Paper
ISSN
24337862
NCID
AA12841878
Journal Title
鳥取大学教育支援・国際交流推進機構教育センター紀要
Current Journal Title
Tottori University Education Center bulletin
Volume
16
Start Page
37
End Page
41
Published Date
2020-03-31
Text Version
Publisher
Rights
注があるものを除き、この著作物は日本国著作権法により保護されています。 / This work is protected under Japanese Copyright Law unless otherwise noted.
Citation
後藤和雄. On the non-differentiability of special exponential sums with M¨obius weight; n=1 μ(n) n einx. 鳥取大学教育支援・国際交流推進機構教育センター紀要. 2020, 16, 37-41.
Department
Affiliated Institutes
Language
English