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

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Inhomogeneous Gevrey ultradistributions and Cauchy problem

Daniela Calvo and L. Rodino

Dipartimento di Matematica, Universita di Torino, via Carlo Alberto 10, 10123 Torino, Italy, e-mail: \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 Liess-Rodino [16]. As an application, we define $(s,\lambda)$-hyperbolic partial differential operators with constant coefficients (for $s>1$), and prove for them the well-posedness 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

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Electronic fulltext finalized on: 10 Jun 2006. This page was last modified: 20 Jun 2011.

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