The Stockwell transform on Gelfand pairs and localization operators

This paper addresses the extension of the Stockwell transform from locally compact abelian groups to Gelfand pairs.

A suitable definition of the Stockwell transform is provided in this framework.

Some major properties of this transform are examined.

Also, the localization operators related to the Stockwell transform are defined and studied.

Mainly, their boundedness and their belonging to Schatten-von Neumann classes are investigated.