Derivatives of flat functions

2018/05/04 by Hiroki Kodama, Kodama, Hiroki, Kazuo Masuda +3
Mathematics · #26A24 (primary) and 26A06 (secondary) #Analytic and geometric function theory #FOS: Mathematics #General Mathematics (math.GM) #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #math.GM #msc:26A06 #msc:26A24

paper · pdf · doi:10.48550/arxiv.1805.01879

5 pages

arxiv created 2018/05/04 · openalex publication_date 2018/05/04 · arxiv updated 2018/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We remark that there is no smooth function f(x) on [0, 1] which is flat at 0 such that the derivative f⁽ⁿ⁾ of any order n≥ 0 is positive on (0,1]. Moreover, the number of zeros of the n-th derivative f⁽ⁿ⁾ grows to the infinity and the zeros accumulate to 0 when n → ∞.

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