Kernel theorems for the spaces of tempered ultradistributions

Abstract

We give a simple proof of the Kernel theorem for the spaces of tempered ultradistributions of Beurling–Komatsu and of Roumieu–Komatsu types, by using the characterization of Fourier–Hermite coefficients of the elements of the spaces. As a consequence of the Kernel theorem, we have that the Weyl transform can be extended on spaces of tempered ultradistributions.

Keywords:

• Hermite coefficients
• Tempered
• Ultradistributions
• Kernel theorem
• Weyl transform

Acknowledgements

The work of the first author was partly supported by Ministry of Science and Environmental Protection of Serbia, grant 144025. The work of the second author was partly supported by Ministry of Science and Environmental Protection of Serbia, grant 144016.