The Recovery Of Bandlimited Function In The Worst Frameworks

Exponential integral function and spline are two basic approximation tools, in this paper, we make use of the methods and means, such as numerical analysis, functional analysis, harmonic analysis, with regard to the bandlimited function f in L p( R ), to carry on error-free recovery in the worst under the framework by using its signals { f (λk )}k∈Z and{ f′(λk )}k∈Z, and get the irregular Hermite-type sampling theorem. At the same time we give the the exact order of confusion errors of Sobolev function class in the sense of order, and obtain an equivalent characterization of multivariate bandlimited function by using k ? degree harmonic cardinal spline.