正规积分小波变换及其连续性

Normalized integral wavelet transform and its continuity

引入并研究了正规积分小波变换W0ψ,讨论了与之相关的算子Dβ,Tα,Ff 及积分算子Λh 的连续性 ,证明了正规积分小波变换W0ψ 是从L2 (R)到C(R×R )∩L2 (R2 )中的线性等距 。

The normalized integral wavelet transform W 0 ψ is introduced. First, the continuity of the related operators D β,T α,F f and integral operator Λ h are discussed. Secondly, it is proved that the normalized integral wavelet transform W 0 ψ is a linear isometry from L 2(R) into C(R×R *)∩L 2(R 2). Lastly, we give the related Parseval identity.