Journal of Applied Mathematics
Volume 2004 (2004), Issue 6, Pages 495-528

Osiris wavelets and Set wavelets

Guy Battle

Department of Mathematics, Texas A&M University, College Station 77843, TX, USA

Received 21 April 2004

Copyright © 2004 Guy Battle. 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.


An alternative to Osiris wavelet systems is introduced in two dimensions. The basic building blocks are continuous piecewise linear functions supported on equilateral triangles instead of on squares. We refer to wavelets generated in this way as Set wavelets. We introduce a Set wavelet system whose homogeneous mode density is 2/5. The system is not orthonormal, but we derive a positive lower bound on the overlap matrix.