Connectivity of wavelets

Abstract

In this paper, path-connectivity of the set of some special wavelets in L^2\left(\mathbb{R}\right), which is the topological geometric property of wavelets, is introduced. In particular, the main progress of wavelet connectivity in the past twenty years is reviewed and some unsolved problems are listed. The corresponding results of high dimension case and other cases are also briefly explained.

Key words： Wavelet; MRA wavelet; S–elementary wavelet; frame wavelet; path-connectivity

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (Grant No. 61471410).

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