Separation of zeros, a hermite interpolation based and a frame based reconstruction algorithms for bandlimited functions

It is shown that if a non-zero function f ∈ Bσ has infinitely many double zeros on the real axis, then there exists at least one pair of consecutive zeros whose distance apart is greater than πσ τ1/4, τ ≈ 5.0625. A Hermite interpolation based and a frame based reconstruction algorithms are provided for reconstructing a function f ∈ Bσ from its nonuniform samples {f(j) (xi): j = 0, 1, …, k − 1, i ∈ Z} with maximum gap condition, sup(xi+1 − xi) = δ < σ1 c1/2kk, where ck is a Wirtinger-Sobolev constant.