Copyright © 2013 Byung Keun Sohn. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be the generalized tempered distributions of -growth with restricted order , where the function grows faster than any linear functions as . We show the convergence of multiresolution expansions of in the test function space of . In addition, we show that the kernel of an integral operator provides approximation order in in the context of shift-invariant spaces.