Affiliation:
1. Department of Mathematics, Indian Institute of Technology Delhi , New Delhi 110016, India
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.
Subject
Mathematical Physics,Statistical and Nonlinear Physics