International Journal of Mathematics and Mathematical Sciences
Volume 2013 (2013), Article ID 190981, 8 pages
Research Article

Multiresolution Expansion and Approximation Order of Generalized Tempered Distributions

Department of Mathematics, Inje University, Kimhae 621-749, Republic of Korea

Received 22 October 2012; Accepted 25 November 2012

Academic Editor: Palle E. Jorgensen

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.


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.