WEIERSTRASS-TYPE FUNCTIONS IN p-ADIC LOCAL FIELDS
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The Weierstrass nowhere differentiable function has been studied often as example of functions whose graphs are fractals in [Formula: see text]. This paper investigates the Weierstrass-type function in the [Formula: see text]-adic local field [Formula: see text] whose graph is a repelling set of a discrete dynamical system, and proves that there exists a linear connection between the orders of the [Formula: see text]-adic calculus and the dimensions of the corresponding graphs.
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1984 ◽
Vol 91
(5)
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pp. 307-308
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2007 ◽
Vol 17
(10)
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pp. 3455-3460
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2009 ◽
Vol 61
(9)
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pp. 1448-1466
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