FourierStieltjes transform defined by induced representation on locally compact groups
Abstract
In this work we extend the FourierStieltjes transform of a vector measure and a continuous function defined on compact groups to locally compact groups. To do so, we consider a representation L of a normal compact subgroup K of a locally compact group G, and we use a representation of G induced by that of L. Then, we define the FourierStieltjes transform of a vector measure and that of a continuous function with compact support defined on G from the representation of G. Then, we extend the Shur orthogonality relation established for compact groups to locally compact groups by using the representations of G induced by the unitary representations of one of its normal compact subgroups. This extension enables us to develop a FourierStieltjes transform in series form that is linear, continuous, and invertible.
 Publication:

arXiv eprints
 Pub Date:
 February 2022
 arXiv:
 arXiv:2202.07055
 Bibcode:
 2022arXiv220207055A
 Keywords:

 Mathematics  Functional Analysis
 EPrint:
 15 pages