In this paper we show how to construct a scaling function and an orthonor-mal wavelet basis from a multiresolution approximation using an operator theoreticmethod.
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The first author got support in part from the fund provided by the University of North Carolina at Charlotte.The second author got support from the National Natural Science Foundation of China and the Science Foundation of Zhejiang Province.
文摘In this paper we show how to construct a scaling function and an orthonor-mal wavelet basis from a multiresolution approximation using an operator theoreticmethod.
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.
