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-existenc...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 aσ-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 aσ-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.
