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The 2-adic derivatives and fractal dimension of Takagi-like function on 2-series field. (English) Zbl 1474.28015

Summary: In this paper, we consider a Takagi-like function on 2-series field and give its 2-adic derivatives by applying Vladimirov operator. The 2-adic derivatives of Takagi-like function with order \(0 < \alpha < 1\) exist and show some fractal feature. Furthermore, both box dimension and Hausdorff dimension of the graph of its derivatives are obtained and equal to \(1 + \alpha\).

MSC:

28A80 Fractals
11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
47G30 Pseudodifferential operators
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