Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques Vol. CXXXIII, No. 31, pp. 175–186 (2006) 

Inhomogeneous Gevrey ultradistributions and Cauchy problemDaniela Calvo and L. RodinoDipartimento di Matematica, Universita di Torino, via Carlo Alberto 10, 10123 Torino, Italy, email: \texttt{calvo@dm.unito.it, rodino@dm.unito.it}Abstract: After a short survey on Gevrey functions and ultradistributions, we present the inhomogeneous Gevrey ultradistributions introduced recently by the authors in collaboration with A. Morando, cf. [7]. Their definition depends on a given weight function $\lambda$ , satisfying suitable hypotheses, according to LiessRodino [16]. As an application, we define $(s,\lambda)$hyperbolic partial differential operators with constant coefficients (for $s>1$), and prove for them the wellposedness of the Cauchy problem in the frame of the corresponding inhomogeneous ultradistributions. This sets in the dual spaces a similar result of Calvo [4] in the inhomogeneous Gevrey classes, that in turn extends a previous result of Larsson [14] for weakly hyperbolic operators in standard homogeneous Gevrey classes. Keywords: Gevrey ultradistributions, inhomogeneous Gevrey classes, Cauchy problem, microlocal analysis Classification (MSC2000): 46F05, 35E15, 35S05 Full text of the article: (for faster download, first choose a mirror)
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