Separation of Zeros, a Hermite Interpolation Based and a Frame Based Reconstruction Algorithms for Bandlimited Functions

摘要

It is shown that if a non-zero function f ∈B_σ has infinitely manyrndouble zeros on the real axis, then there exists at least one pair of consecutivernzeros whose distance apart is greater than Hermite interpolation based and a frame based reconstruction algorithmsrnare provided for reconstructing a function f ∈B_σ from its nonuniform samplesrn{f~((j))(x_i) : j = 0, 1,…, k -1; I ∈ Z} with maximum gap condition,rnsup(x_i+1 - x_i) = δ<1/σ , where ck is a Wirtinger-Sobolev constant.