Gradient-Orthonormal Bases of Momentum-Entire Wavelets in Odd Dimension
Guy Battle *
Texas A&M University, College Station, TX 77843-3368, USA.
*Author to whom correspondence should be addressed.
Abstract
We construct gradient-orthonormal bases of momentum-entire wavelets in dimension n in the case where n is odd. The scale factor is 3√2 and the coherence on a given scale is based on the propagator exp 
.This propagator can be described in terms of two one-variable functions. One of them is the Airy function, while the other satisfies an ordinary differential equation less familiar than the Airy equation. This construction is part of our on-going quest for compactly supported, gradient-orthonormal wavelets that have some kind of coherence on a given scale.
Keywords: Fourier transform, wavelets, complex variables.