A gradient-projective basis of compactly supported wavelets in dimension n > 1 Academic Article uri icon

abstract

  • AbstractA 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 $sumlimits_chi {(int_{mathbb{R}^n } {
    abla f cdot }
    abla W_chi ^* )} W_chi $ converges to f with respect to the norm (left| {
    abla ( cdot )}
    ight|_{L^2 (mathbb{R}^n )} ) . 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 functions on n such that

published proceedings

  • Open Mathematics

author list (cited authors)

  • Battle, G.

publication date

  • January 1, 2013 11:11 AM