کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4641997 1341325 2008 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Subdivisions with infinitely supported mask
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Subdivisions with infinitely supported mask
چکیده انگلیسی

In this paper we investigate the convergence of subdivision schemes associated with masks being polynomially decay sequences. Two-scale vector refinement equations are the formφ(x)=∑α∈Za(α)φ(2x-α),x∈R,where the vector of functions φ=(φ1,…,φr)Tφ=(φ1,…,φr)T is in (L2(R))r(L2(R))r and a≕(a(α))α∈Za≕(a(α))α∈Z is polynomially decay sequence of r×rr×r matrices called refinement mask. Associated with the mask a   is a linear operator on (L2(R))r(L2(R))r given byQaf(x)≔∑α∈Za(α)f(2x-α),x∈R,f=(f1,…,fr)T∈(L2(R))r.By using same methods in [B. Han, R. Q. Jia, Characterization of Riesz bases of wavelets generated from multiresolution analysis, manuscript]; [B. Han, Refinable functions and cascade algorithms in weighted spaces with infinitely supported masks, manuscript]; [R.Q. Jia, Q.T. Jiang, Z.W. Shen, Convergence of cascade algorithms associated with nonhomogeneous refinement equations, Proc. Amer. Math. Soc. 129 (2001) 415–427]; [R.Q. Jia, Convergence of vector subdivision schemes and construction of biorthogonal multiple wavelets, in: Advances in Wavelet, Hong Kong,1997, Springer, Singapore, 1998, pp. 199–227], a characterization of convergence of the sequences (Qanf)n=1,2,… in the L2L2-norm is given, which extends the main results in [R.Q. Jia, S.D. Riemenschneider, D.X. Zhou, Vector subdivision schemes and multiple wavelets, Math. Comp. 67 (1998) 1533–1563] on convergence of the subdivision schemes associated with a finitely supported mask to the case in which mask a   is polynomially decay sequence. As an application, we also obtain a characterization of smoothness of solutions of the refinement equation mentioned above for the case r=1r=1.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 214, Issue 1, 15 April 2008, Pages 288–303
نویسندگان
, ,