... Annals of Mathematics, 158 (2003), 679–710 Approximating a bandlimited function using very coarsely quantized data: A family of stable sigma-delta modulators of arbitrary order By Ingrid Daubechies ... DEVORE , Approximating a bandlimited function using very coarsely quantized data: Improved error estimates in sigma-delta modulation, J Amer Math Soc., to appear ¨ ¨ C S Gunturk, J C Lagarias, and ... both cases, one can prove that there exists a bounded set Aa ⊂ R2 so that if |xn | ≤ a for all n, and (u0 , v0 ) ∈ Aa , then (un , ) ∈ Aa for all n ∈ N; see [19] APPROXIMATING A BANDLIMITED FUNCTION...