高维有噪频谱有限函数的外推

Extrapolation of Multidimensional Band-Limited Functions with Noises

给出的定理既适合于一维与高维，又适合于有噪与无噪的频谱有限函数的外推，是对SanzHuang两个猜想的改进，同时讨论了外推函数与真函数的逼近关系.对于一个一维或高维Ω频谱有限函数f，如果仅知道它在局部区域T上的有噪测量值，用集合{g:g是Ω频谱有限函数，在T上|g(t)-(t)|≤δ}(δ≥0)中L2范数最小的元素hδ,作为外推函数，给出了关于它的逼近定理及其范数逼近公式，并且给出定理说明这一外推函数hδ。

A method for the extrapolation of mul tidimensional bandlimited functions is presented, which can be used for the extrapolation wit h noises or nonoises and is an improvement of SanzHuang's two conject ures about the extrapolation of bandlimited functions. For a Ω bandlimited function f, if its local values  with noises or nonoises are measured ， the minnorm function hδ, i n {g:g is a Ω bandlimit ed function， |g(t)(t)|≤δ in local field  T }（ δ≥0) is regarded as an extrapolation of  . A formula about the computation of hδ, an d its norm was given, and the theorem showing that the approach of hδ, to f mainly depends on the error δ was also given.