Paley-Wiener-type theorem for polynomial ultradifferentiable functions

Abstract

The image of the space of ultradifferentiable functions with compact supports under Fourier-Laplace transformation is described. An analogue of Paley-Wiener theorem for polynomial ultradifferentiable functions is proved.

Keywords

• ultradifferentiable function
• ultradistribution
• polynomial test function
• paley-wiener-type theorem