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Approximation of rough functions

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

Description

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
URI: http://hdl.handle.net/1885/112240
Source: Journal of Approximation Theory
DOI: 10.1016/j.jat.2016.04.003

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