The Recovery of Multivariate Bandlimited Function via Polyharmonic Cardinal Spline
Luo Xin-jian · Journal of Sichuan Normal University · 2010
Spline function and band limited function are two important tools for approximation.In this paper,the error-free recovery of multivariate bandlimited function in L2-scale is discussed by using polyharmonic cardinal spline.The two important approximation tools are linked.Furthermore,an equivalent form about mulitivariate bandlimited is obtained.Some result of literature are generalized.Meanwhile,the best approximation of L2(Rd) in L2-scale is made by using the multivariate bandlimited function space(Paley-Wiener space) and k-degree harmonic cardinal spline in L2(Rd) space,respectively,and the link of the two extremes is established.