Gabor System Based on the Unitary Dual of the Heisenberg Group

Abstract

In this paper Gabor system of certain type based on the unitary dual of the Heisenberg group H n is introduced and a sufficient condition is obtained for the Gabor system to be a Bessel sequence for L 2 (R * , B 2 ; dκ) using the Schrödinger representation of H n , where B 2 denotes the class of Hilbert-Schmidt operators on L 2 (R n ) and dκ denotes the Haar measure on R * . Further a necessary and sufficient condition is provided for the Gabor system to be an orthonormal system, a Parseval frame sequence, a frame sequence and a Riesz sequence.