### A gradient-projective basis of compactly supported wavelets in dimension n > 1

A given set W = W X of n-variable class C 1 functions is a gradient-projective basis if for every tempered distribution f whose gradient is square-integrable, the sum $\sum _{\chi}\left({\int}_{{\mathbb{R}}^{n}}\nabla f\xb7\nabla {W}_{\chi}^{*}\right){W}_{\chi}$ converges to f with respect to the norm ${\u2225\nabla (\xb7)\u2225}_{{L}^{2}\left({\mathbb{R}}^{n}\right)}$ . The set is not necessarily an orthonormal set; the orthonormal expansion formula is just an element of the convex set of valid expansions of the given function f over W. We construct a gradient-projective basis W = W x of compactly supported class C 2−ɛ functions on ℝn such that [...]...