Generalized Wavelet Decompositions of Bivariate Functions
Charles K. Chui, Xin Li · Proceedings of the American Mathematical Society · 1994
The objective of this paper is to introduce an integral transform of wavelet-type on ${L^2}({R^2})$ that can be applied to decompose the space ${L^2}({R^2})$ into a direct sum of subspaces, each of which is identified as ${L^2}(R)$. Projections from ${L^2}({R^2})$ onto these subspaces are also discussed. Moreover, wavelet expansions for functions in ${L^2}({R^2})$ are derived in terms of wavelet bases of ${L^2}(R)$.