Inhomogeneous Gevrey ultradistributions and Cauchy problem

After a short survey on Gevrey functions and ultradistributions, we present the inhomogeneous Gevrey ultradistributions, defined as the dual space of the inhomogeneous Gevrey classes. They are an extension of the standard homogeneous Gevrey case by means of the Fourier transform, and are based on a weight function, satisfying suitable hypotheses. As an application, we define a suitable class of weakly hyperbolic operators with constant coefficients, and prove for them the well-posedness of the Cauchy problem in the frame of the corresponding inhomogeneous ultradistributions. Stampato nel mese di Aprile 2005 presso il Centro Stamp