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- W3147628505 abstract "We investigate the solutions of vector refinement equations with polynomially decaying masks, which play an important role for characterizations of Riesz wavelet bases and biorthogonal wavelets. A vector refinement equation is of the form: = ∑ α∈Zs a(α)(2·α), where = (1,...,r)T is the unknown vector of functions on Rs, a := (a(α))α∈Zs is a polynomially decaying sequence of r × r matrices called refinement mask. Associated with the mask a is a linear operator Qa defined on (Lp(Rs))r by: Qaf := ∑α∈Zs a(α)f(2·α). The iterative scheme (Qnaf)n=1,2,... is called a vector subdivision scheme or a vector cascade algorithm. In this paper, we shall prove that if the vector subdivision scheme converges in (L2(Rs))r, then its resulting limit function automatically has polynomial decay. Moreover, under some appropriate conditions on the initial function, the convergence rates of the vector subdivision scheme will be given." @default.
- W3147628505 created "2021-04-13" @default.
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- W3147628505 date "2012-01-01" @default.
- W3147628505 modified "2023-09-23" @default.
- W3147628505 title "Vector subdivision schemes with polynomially decaying masks" @default.
- W3147628505 hasPublicationYear "2012" @default.
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