Single wavelets in n-dimensions

Under very minimal regularity assumptions, it can be shown that 2(n) - 1 functions are needed to generate an orthonormal wavelet basis for L-2(R-n). In a recent paper by Dai et al. it is shown, by abstract means, that there exist subsets K of R-n such that the single function psi, defined by <(psi)over cap> = chi(K), is an orthonormal wavelet for L-2(R-n). Here we provide methods for constructing explicit examples of these sets. Moreover; we demonstrate that these wavelets do not behave like their one-dimensional counterparts.