The Recovery Of Multivariate Bandlimited Function In The Worst Frameworks

In this paper, I make use of the methods, such as real analysis, harmonic analysis, numerical analysis, functional analysis, Hilbert transform, have done two works:(1) reconstruct the function f of B2σ,p (Rd) in the worst framework by using its signal sampling sequences {f (λn)}n∈Zd and {f’j (λn)]n∈Zd and get the multidimensional sampling theorem of one order Hermite type and the order of aliasing error.(2) reconstruct the function f of B3σ,p(Rd) in the worst framework by using its signal sampling sequences and and get the multidimensional sampling theorem of two order Hermite type and the order of aliasing error.