Inhomogeneous Gevrey classes and ultradistributions
Starting from the definition of inhomogeneous Gevrey classes given by \textit{O. Liess} and \textit{L. Rodino} [Boll. Unione Mat. Ital., VI. Ser., C, Anal. Funz. Appl. 3, 233--323 (1984; Zbl 0557.35131)], the authors introduce the non-quasi-analytic inhomogeneous Gevrey classes of Roumieu type, denoted by \(G^{s, \lambda}.\) Such a class of ultradifferentiable functions is always between two standard Gevrey classes, and therefore contains non-trivial functions with compact support. \(G^{s, \lambda}\) need not be an algebra under pointwise multiplication, except in the case that the function \(\lambda\) satisfies the ring condition. The lack of the ring condition is fundamental in order to include the study the multianisotropic Gevrey classes. Topological properties of these spaces are studied and dual spaces are introduced. Under the Fourier-Laplace transform, the dual of \(G^{s, \lambda}\) is isomorphic to a weighted LF-space of entire functions.
scientific article; zbMATH DE number 2107217
scientific article