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Convergence Rates of Cascade Algorithms with Infinitely Supported Masks

  • Jianbin Yang (a1) and Song Li (a1)
Abstract

We investigate the solutions of refinement equations of the form

where the function ϕ is in Lp (ℝ s )(1 ≤ p ≤ ∞), a is an infinitely supported sequence on ℤ s called a refinement mask, and M is an s × s integer matrix such that lim n→1 M n = 0. Associated with the mask a and M is a linear operator Qa ,M defined on Lp (ℝ s ) by Qa ,0 := Σα∈ℤ s a(α)ϕ 0(M · –α). Main results of this paper are related to the convergence rates of in Lp (ℝ s ) with mask a being infinitely supported. It is proved that under some appropriate conditions on the initial function ϕ 0, converges in Lp (ℝ s ) with an exponential rate.

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References
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