Hilbert空间L^2(R^n)上正规窗口的Fourier变换

Normalized windowed Fourier transform in Hilbert space L^2(R)~n

引入并研究了Hilbert空间L2(Rn)上正规窗口的Fourier变换,讨论了一个L2(Rn)函数的正规窗口的Fourier变换的有界性和连续性,证明了正规窗口Fourier变换的等距性质,并且给出了一个L2(Rn)函数在弱收敛意义下和在强收敛意义下成立的重构公式.

The normalized windowed Fourier transform in L^2（R^n） is studied. It is discussed that bounded and continuous properties of the normalized windowed Fourier transform of a L^2（R^n） function. It is proved that the isometric property of normalized windowed Fourier transform. The reconstruction formulas of a L^2（R^n） function in the weak topology and in the strong topology, respectively, is given.