Approximation of rough functions
-
Altmetric Citations
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.
Collections | ANU 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 |
Access Rights: | Open Access |
Download
File | Description | Size | Format | Image |
---|---|---|---|---|
Barnsley M F et al Approximation of rough 2016.pdf | 230.19 kB | Adobe PDF | ![]() |
Items in Open Research are protected by copyright, with all rights reserved, unless otherwise indicated.
Updated: 19 May 2020/ Responsible Officer: University Librarian/ Page Contact: Library Systems & Web Coordinator