Geodesic
Inhomogeneous Gevrey ultradistributions and Cauchy problem
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 31 (2006), p. 175 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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.
Classification : 46F05 35E15 35S05
Keywords: Gevrey ultradistributions, inhomogeneous Gevrey classes, Cauchy problem, microlocal analysis 
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     author = {Daniela Calvo and L. Rodino},
     title = {Inhomogeneous {Gevrey} ultradistributions and {Cauchy} problem},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {175 },
     year = {2006},
     volume = {31},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASS_2006_31_a13/}
}
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Daniela Calvo; L. Rodino. Inhomogeneous Gevrey ultradistributions and Cauchy problem. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 31 (2006), p. 175 . http://geodesic.mathdoc.fr/item/BASS_2006_31_a13/