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

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  • Hua, Qiu
  • Weiyi, Su

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.

Suggested Citation

  • Hua, Qiu & Weiyi, Su, 2006. "Weierstrass-like functions on local fields and their p-adic derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 958-965.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:4:p:958-965
    DOI: 10.1016/j.chaos.2005.09.017
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    Cited by:

    1. Wu, Bo & Su, Weiyi, 2009. "Eigenfrequencies of nonisotropic fractal drums," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3210-3218.

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