Stockwell transform for Boehmians

Abstract

In this article, we state and prove a convolution theorem for the Stockwell transform on L ²(ℝ) and characterize the range of the transform. Applying the convolution theorem, we construct a Boehmian space which contains the Stockwell transforms of all square-integrable Boehmians. We prove that the extended Stockwell transform on square-integrable Boehmians is consistent with the classical Stockwell transform on square-integrable functions and is linear, one to one, continuous with respect to δ-convergence as well as Δ-convergence. We also characterize the range of the extended Stockwell transform on the space of square-integrable Boehmians.

Keywords:

• Boehmians
• convolution
• Stockwell transform

AMS Subject Classification::

• 44A15
• 44A35

Acknowledgements

The author expresses his gratitude to the referee for valuable suggestions.