transform from to meaning in English

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And by far , most theories of wavelet analysis are established in , but this method is rare to be known and exists defects in the reproducing kernel space with good properties . then in the reproducing kernel space , isometric isomorphism of relation is founded between and by differential operator . and starting from the haar basis , multi - resolution analysis inis gived by folding method ; then multi - resolution analysis and orthonormal wavelet in are obtained through integral transform from to . then the reproducing kernel space can be expressed by wavelet spaces
于是，在再生核空间中，利用积分算子建立了空间与hilbert空间的等距同构关系；并且从haar小波出发，由折叠法实现的空间中多尺度分析通过积分变换得到中多尺度分析和正交小波，使得再生核空间可以由小波空间来刻划；从而对空间中的函数，给出了小波逼近具体表达式和相应的采样公式，形式简单易于数值分析。