کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4607998 1337896 2008 21 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Internal structure of the multiresolution analyses defined by the unitary extension principle
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Internal structure of the multiresolution analyses defined by the unitary extension principle
چکیده انگلیسی

We analyze the internal structure of the multiresolution analyses of L2(Rd)L2(Rd) defined by the unitary extension principle (UEP) of Ron and Shen. Suppose we have a wavelet tight frame defined by the UEP. Define V0V0 to be the closed linear span of the shifts of the scaling function and W0W0 that of the shifts of the wavelets. Finally, define V1V1 to be the dyadic dilation of V0V0. We characterize the conditions that V1=W0V1=W0, that V1=V0∔W0V1=V0∔W0 and V1=V0⊕W0V1=V0⊕W0. In particular, we show that if we construct a wavelet frame of L2(R)L2(R) from the UEP by using two trigonometric filters, then V1=V0∔W0V1=V0∔W0; and show that V1=W0V1=W0 for the BB-spline example of Ron and Shen. A more detailed analysis of the various ‘wavelet spaces’ defined by the BB-spline example of Ron and Shen is also included.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Approximation Theory - Volume 154, Issue 2, October 2008, Pages 140–160
نویسندگان
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