Shannon-like Parseval Frame Wavelets on Some Two step Nilpotent Lie Groups
We construct Shannon-like Parseval frame wavelets on a class of non commutative two-step nilpotent Lie groups. Our work was inspired by a construction given by Azita Mayeli on the Heisenberg group. The tools used here are representation theoretic. However, a great deal of Gabor theory is used for the construction of the wavelets. The construction obtained here is very explicit, and we are even able to compute an upper bound for the L2 norm for these Parseval frame wavelets.
Oussa, V. (2013). Shannon-like Parseval Frame Wavelets on Some Two step Nilpotent Lie Groups. International Journal of Pure and Applied Mathematics, 84 (4), 397-418. https://doi.org/10.12732/ijpam.v84i4.10
Virtual Commons Citation
Oussa, Vignon (2013). Shannon-like Parseval Frame Wavelets on Some Two step Nilpotent Lie Groups. In Mathematics Faculty Publications. Paper 53.
Available at: http://vc.bridgew.edu/math_fac/53