The S-transform on spaces of type S

Abstract

It is shown that the S-transform with the Gaussian window is a continuous linear map of the space of type S defined on ℝ into the space of type [Stilde] defined on ℝ×(ℝ∖{0}). The S-transforms of certain ultradifferentiable functions are also investigated.

Keywords:

• spaces of type S
• S-transform
• ultradifferentiable functions
• ultradistributions
• wavelet transform

AMS Subject Classification :

• 42C40
• 46F12

Acknowledgements

This work is supported by the University Grants Commission (UGC), New Delhi, India (F.No. 37-543/2009(SR)).