The wavelet dimension function is the trace function of a shift-invariant system |
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| Authors: | Amos Ron Zuowei Shen |
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| Institution: | Computer Sciences Department, University of Wisconsin-Madison, 1210 West Dayton, Madison, Wisconsin 53706 ; Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260 |
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| Abstract: | In this note, we observe that the dimension function associated with a wavelet system is the trace of the Gramian fibers of the shift-invariant system generated by the negative dilations of the mother wavelets. When this shift-invariant system is a tight frame, each of the Gramian fibers is an orthogonal projector, and its trace, then, coincides with its rank. This connection leads to simple proofs of several results concerning the dimension function, and the arguments extend to the bi-frame case. |
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| Keywords: | Dimension function frames multiresolution analysis wavelets |
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