Construction of Biorthogonal B-spline Type Wavelet Sequences with Certain Regularities

نویسنده

  • Tian-Xiao He
چکیده

In this paper we study a refinement equation of the form φ(x) = ∑ n∈Z hnφ(2x− n), where {hn} is a finitely supported sequence. Let the symbol of the sequnce m(z) := 1 2 ∑ n hnz n take the form m(z) = ( 2 ) Nzk ′∑k j=0 ajz j where ∑ j aj = 1 and ∑ j(−1)aj 6= 0. Under the assumption (∑ 0≤odd j≤k |aj | )2 + (∑ 0≤even j≤k |aj | )2 < 22N−1 we show that the corresponding φ is in L2. Then the B-spline type wavelet sequences that possess the largest possible regularities and required vanishing moments are characterized. AMS Subject Classification: 39A70, 41A80, 65B10.

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تاریخ انتشار 2005