Generalized self-similarity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:230

Article

Cabrelli, CA ; Molter, UM

关键词: self-similarity;    functional equation;    dilation equation;    refinement equation;    wavelets;    fixed points;    fractals;    inverse problem for fractals;   

DOI  :  10.1006/jmaa.1998.6200

来源: Elsevier

【 摘 要 】

We prove the existence of L-P functions satisfying a kind of self-similarity condition. This is achieved by solving a functional equation by means of the construction of a contractive operator on an appropriate functional space. The solution, a fixed point of the operator, can be obtained by an iterative process, making this model very suitable to use in applications such as fractal image and signal compression. On the other hand, this generalized self-similarity equation includes matrix refinement equations of the type f(x) = Sigma c(k)f(Ax - k) which are central in the construction of wavelets and multiwavelets. The results of this paper will therefore yield conditions for the existence of L-P-refinable functions in a very general setting. (C) 1999 Academic Press.

【 授权许可】

Free