Approximation of rough functions

JOURNAL OF APPROXIMATION THEORY

卷:209

Article

Barnsley, M. F.¹  Harding, B.¹  Vince, A.²  Viswanathan, P.^1,3 

[1] Australian Natl Univ, Canberra, ACT 2601, Australia

[2] Univ Florida, Dept Math, Gainesville, FL 32611 USA

[3] Indian Inst Technol, Dept Math, New Delhi 110016, India

关键词: Functional equations;    Fractal interpolation;    Iterated function system;    Fractal geometry;    Fourier series;   

DOI  :  10.1016/j.jat.2016.04.003

来源: Elsevier

【 摘 要 】

For given p is an element of [1, infinity] and g is an element of L-P (R), we establish the existence and uniqueness of solutions f is an element of L-P (R), to the equation f (x) - af (bx) = g(x), where a is an element of R, b is an element of R \ {0}, and vertical bar a vertical bar not equal vertical bar b vertical bar(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. (C) 2016 The Author(s). Published by Elsevier Inc.

【 授权许可】

Free