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Evaluation of Sugarcane Seedlings for Resistance to the Sugarcane Borer, Diatraea Saccharalis (F.).
Subdivisions with infinitely supported mask
AbstractIn this paper we investigate the convergence of subdivision schemes associated with masks being polynomially decay sequences. Two-scale vector refinement equations are the formÏ(x)=âαâZa(α)Ï(2x-α),xâR,where the vector of functions Ï=(Ï1,âŠ,Ïr)T is in (L2(R))r and aâ(a(α))αâZ is polynomially decay sequence of rĂr matrices called refinement mask. Associated with the mask a is a linear operator on (L2(R))r given byQaf(x)ââαâZa(α)f(2x-α),xâR,f=(f1,âŠ,fr)Tâ(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) 415â427]; [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. 199â227], a characterization of convergence of the sequences (Qanf)n=1,2,⊠in the L2-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) 1533â1563] 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=1
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