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,在再生核空間中,利用積分算子建立了空間與hilbert空間的等距同構(gòu)關(guān)系;并且從haar小波出發(fā),由折疊法實現(xiàn)的空間中多尺度分析通過積分變換得到中多尺度分析和正交小波,使得再生核空間可以由小波空間來刻劃;從而對空間中的函數(shù),給出了小波逼近具體表達式和相應的采樣公式,形式簡單易于數(shù)值分析。