Self-Affine Fractal Functions and Wavelet Series☆☆☆
Self-Affine Fractal Functions and Wavelet Series☆☆☆
复制标题
DOI：
10.1006/jmaa.1999.6614
复制
发表时间：
1999-12
影响因子：
1.3
通讯作者：
P. Singer;Peter Zajdler
中科院分区：
文献类型：
--
作者：
P. Singer;Peter Zajdler
摘要考虑由小波型级数∑g∈g c g ψ(g−1 (x))表示的函数，其中g是由仿射函数L 1，…，L n生成的群，ψ是分段仿射的。利用这些函数，我们描述了Barnsley等人先前研究的自仿射分形函数。我们计算了它们的全局和局部Holder指数，并研究了它们的不可微点。给出了各种连续不可微函数和奇异函数的小波表示。另一个应用是构造在每个点具有指定的局部Holder指数的函数。
Abstract We consider functions represented by series ∑ g ∈ G c g ψ( g − 1 ( x )) of wavelet-type, where G is a group generated by affine functions L 1 ,…, L n and ψ is piecewise affine. By means of those functions we characterize the class of self-affine fractal functions, previously studied by Barnsley et al. We compute their global and local Holder exponents and investigate points of non-differentiability. Wavelet-representations for various continuous nowhere differentiable and singular functions are presented. Another application is the construction of functions with prescribed local Holder exponents at each point.