多元函数的窗口Fourier变换反演公式

摘要

用算子论和积分论的方法研究了多元函数的规范窗口Fourier变换,证明了多元函数f∈L2（Rd）的规范窗口Fourier变换Twwinf和算子Twwin的若干重要性质.通过L2（Rd）值函数的Bochner积分,构造了函数f∈L2（Rd）的强逼近序列{Fn}n∞=1,证明了这个序列以范数收敛于给定函数f,进而得到多元函数的规范窗口Fourier变换的一个强反演公式.%By using operator and integral theory,normalized windowed Fourier transformations of multivariate functions are studied.Some properties of the function Twinw f and the operator Twinw are proved.With Bochner integral in L2（Rd）,a strong approximation sequence Fn∞n=1 of f∈L2（Rd） is constructed and is proved to be convergent to the given function f,and a strong inversion formula of normalized windowed Fourier transformation of a multivariate function is then established.