L^2(R^d)中的积分小波变换及其反演公式

Integral wavelet transform in L^2 (R^d) and its reconstruction formulas

研究了L2(Rd)中的积分小波变换.利用算子论和积分论的方法,讨论了L2(Rd)中函数的积分小波变换的有界性和连续性,证明了积分小波变换的等距性质,并给出了积分小波变换在强收敛意义和弱收敛意义下的重构公式.

The integral wavelet transform in L2（Rd） is studied.By using operator and integral theory,the bound-edness and continuity of integral wavelet transformation of an L2（Rd） function are discussed,the isometric property of integral wavelet transform is proved,and the reconstruction formulas in the strong topology and in the weak topology are established,respectively.