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| Keywords | non-differentiable
exponential sums
M¨obius function
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| 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.
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| Publisher | 鳥取大学教育支援・国際交流推進機構教育センター
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| Content Type |
Departmental Bulletin Paper
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| ISSN | 24337862
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| NCID | AA12841878
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| 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
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| Current Journal Title |
Tottori University Education Center bulletin
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| Volume | 16
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| Start Page | 37
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| End Page | 41
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| Published Date | 2020-03-31
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| Text Version |
Publisher
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| 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.
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| 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.
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| Department |
Affiliated Institutes
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| Language |
English
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