A four dimensional continuous wavelet transform
Mahya Ghandehari, A.O. Syzdykova, Keith Taylor · Contemporary mathematics - American Mathematical Society · 2013
The space of real square matrices of fixed size is a vector space whose dimension is a perfect square and the invertible matrices constitute a dense open subset of this vector space. As a result, the locally compact group formed as the semi-direct product of the additive group of all matrices acted on by the invertible matrices has, up to uniqueness, just one square-integrable irreducible unitary representation. This representation is the source of a continuous wavelet transform in each Euclidean space whose dimension is a perfect square. In dimension 1, this is the classical continuous wavelet transform. An explicit formulation is worked out in four dimensions and a method for constructing associated discrete frames is presented.