A Paley–Wiener type theorem for generalized non-quasianalytic classes
Volume 208 / 2012
Studia Mathematica 208 (2012), 31-46
MSC: 46F05, 47F05, 35B65, 35H10.
DOI: 10.4064/sm208-1-3
Abstract
Let $P$ be a hypoelliptic polynomial. We consider classes of ultradifferentiable functions with respect to the iterates of the partial differential operator $P(D)$ and prove that such classes satisfy a Paley–Wiener type theorem. These classes and the corresponding test spaces are nuclear.
