International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 64, Pages 3435-3444

Refinement equations for generalized translations

W. Christopher Lang

Department of Mathematics, School of Natural Sciences, Indiana University Southeast, New Albany 47150, IN, USA

Received 5 March 2004

Copyright © 2004 W. Christopher Lang. 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.


We study refinement equations which relate the dilation of a function with generalized translates of the function, consisting of convolutions against certain kernels including Cauchy and Gaussian densities; solutions are expressed in terms of solutions of the corresponding refinement equation involving ordinary translation.