Momentum-Entire Wavelets with Discrete Rotational Symmetries in 2D

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.