| 1 | On the direct path problem of s-elementary frame wavelets显示文摘In this paper, we discuss the path-connectivity between two s-elementary normalized tight frame wavelets via the so-called direct paths. We show that the existence of such a direct path is equivalent to the non-existence of an atom of a σ-algebra defined over the defining sets of the corresponding frame wavelets, using a mapping defined by the natural translation and dilation operations between the sets. In particular, this gives an equivalent condition for the existence of a direct path between two s-elementary wavelets. | DAI XingDe 1 , DIAO YuanAn 1 & GUO XunXiang 2,1 Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, USA 2 Department of Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China | 2010 | Science China Mathematics2010，53，12： | 1 |
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