International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 64, Pages 3435-3444
doi:10.1155/S0161171204403135
Refinement equations for generalized translations
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.
Abstract
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.