Approximation of rough functions

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• 作者：M.F. Barnsley^a ; ^{michael.barnsley@anu.edu.au" class="auth_mail" title="E-mail the corresponding author} ; B. Harding^a ; ^{brendan.harding@anu.edu.au" class="auth_mail" title="E-mail the corresponding author} ; A. Vince^b ; ^{avince@ufl.edu" class="auth_mail" title="E-mail the corresponding author} ; P. Viswanathan^a ; ¹ ; ^{amritaviswa@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：26A15 ; 26A18 ; 26A27 ; 42A38 ; 39B12
• 刊名：Journal of Approximation Theory
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：209
• 期：Complete
• 页码：23-43
• 全文大小：624 K

文摘

For given p∈[1,∞]$p\in [1,\infty ]$ and g∈L^p(R)$g\in L^p\left(\mathbb{R}\right)$, we establish the existence and uniqueness of solutions f∈L^p(R)$f\in L^p\left(\mathbb{R}\right)$, to the equation where a∈R$a\in \mathbb{R}$, b∈R∖{0}$b\in \mathbb{R}\setminus \left\{0\right\}$, and |a|≠|b|^1/p$\left|a\right|\ne {\left|b\right|}^{1/p}$. 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.