Momentum-Entire Wavelets with Discrete Rotational Symmetries in 2D
Journal of Advances in Mathematics and Computer Science · pp. 315–329 · Published 29 Apr 2013
10.9734/BJMCS/2013/2481Abstract
We introduce wavelet bases consistent with the eigenspaces of the action of rotation by the angle 2π / N in dimension d = 2. Our particular construction yields wavelets that are momentrum-entire (a property weaker than the compact support property). The orthogonality of wavelets in a given eigenspace is based on an inner product that depends on the eigenspace, while the eigenspaces themselves form a super-orthogonal system over a certain family of Hilbert spaces. (We describe this notion in the Introduction.) The existence of a gradient-orthonormal basis of momentum-entire wavelets is an issue that remains open.
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