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Approximation of rough functions

Barnsley, M. F.; Harding, B.; Vince, A.; Viswanathan, P.


For given p ∈ [1,∞] and g ∈ Lᵖ(R), we establish the existence and uniqueness of solutions f ∈ Lᵖ(R), to the equation f (x) − a f (bx) = g(x), where a ∈ R, b ∈ R\ {0}, and |a| ̸= |b|1/p. Solutions include well-known nowhere differentiable functions such as those of Bolzano, Weierstrass, Hardy, and many others. Connections and consequences in the theory of fractal interpolation, approximation theory, and Fourier analysis are established.

CollectionsANU Research Publications
Date published: 2016-09
Type: Journal article
Source: Journal of Approximation Theory
DOI: 10.1016/j.jat.2016.04.003
Access Rights: Open Access


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