Abstract
In this article, we study two different types of operators, the localization operator and Weyl transform, on the reduced Heisenberg group with multidimensional centre G. The group G is a quotient group of non-isotropic Heisenberg group with multidimensional centre Hm by its centre subgroup. Firstly, we define the localization operator using a wavelet transform on G and obtain the product formula for the localization operators. Next, we define the Weyl transform associated to the Wigner transform on G with the operator-valued symbol. Finally, we have shown that the Weyl transform is not only a bounded operator but also a compact operator when the operator-valued symbol is in Lp, 1 ≤ p ≤ 2, and it is an unbounded operator when p > 2.
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