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-existe...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.展开更多
基金supported by Natural Science Foundation of USA (Grant No. DMS-0712958)supported by SWUFE’s Key Subjects Construction Items Funds of 211 Project+1 种基金the Natural Science Foundation of Jiang Xi Province, China (Grant No. 2008GZS0024)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry of China (Grant No.[2008]890)
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.
