摘要
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.
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.
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
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)
