Weierstrass-like functions on local fields and their p-adic derivatives

Qiu Hua and Su Weiyi

Chaos, Solitons & Fractals, 2006, vol. 28, issue 4, 958-965

Abstract: The concept of derivatives of functions plays a key role in the study of local fields. Such a definition was given by virtue of pseudo-differential operators by Su in 1992 [Su W. Pseudo-differential operators and derivatives on locally compact Vilenkin groups. Sci China (series A) 1992;35(7A):826–36; Su W. Gibbs–Butzer derivatives and the applications. Numer Funct Anal Optimiz 1995;16(5–6):805–24]. In this paper, a kind of Weierstrass-like functions in the p-series local fields are found, these Weierstrass-like functions [Falconer KJ. Fractal geometry: mathematical foundations and applications. New York: John Wiley & Sons, Inc.; 1990. [1]] are continuous, and m order differentiable with m<1 but not one order differentiable at any point in its domain.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:28:y:2006:i:4:p:958-965

DOI: 10.1016/j.chaos.2005.09.017

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