Journal of Applied Mathematics
Volume 2004 (2004), Issue 6, Pages 495-528
Osiris wavelets and Set wavelets
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 . The system is not orthonormal, but we
derive a positive lower bound on the overlap matrix.