Journal of the
Korean Mathematical Society JKMS

We provide a constructive wavelet decomposition
of $L_p$ ($1\leq p\leq\infty$) into box splines. To calculate
wavelet coefficients, we apply the local polynomial $L_2$-approximation and
then quasi-interpolation techniques. Furthermore, we characterize the Besov
space, $\Baq{}$ ($q=(\alpha/d+1/p)^{-1}$), by the constructive wavelet
coefficients with an explicit form. DeVore {\it et al.\rm} have studied this
characterization with a different proof; however, they have used a
nonconstructive local approximation rather than the local $L_2$-approximation
when $0 be directly employed for numerical implementations.

Keywords: Besov spaces, box splines, quasi-interpolants, wavelet decompos- itions

MSC numbers: 65D05, 65D07, 65D15, 68U10, 41A15