LIU Long-fei1,2, YU Bao-min2, CAO Huai-xin1
(1 College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710062, Shaanxi, China; 2 College of Mathematics and Information Science, Weinan Teachers University, Weinan 714000, Shaanxi, China)
Abstract:
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.
KeyWords:
normalized windowed Fourier transformation; reconstruction formula; approximate sequence
