IJPAM: Volume 84, No. 4 (2013)

SHANNON-LIKE PARSEVAL FRAME WAVELETS
ON SOME TWO STEP NILPOTENT LIE GROUPS

Vignon Oussa
Department of Mathematics
Bridgewater State University
Bridgewater, MA 02325, USA


Abstract. 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.

Received: January 15, 2013

AMS Subject Classification: 22E25

Key Words and Phrases: nilpotent, Lie groups, wavelets

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DOI: 10.12732/ijpam.v84i4.10 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 84
Issue: 4