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Gevrey local solvability in locally integrable structures
Authors:Francesco Malaspina  Fabio Nicola
Institution:1. Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy
Abstract:We consider a locally integrable real-analytic structure, and we investigate the local solvability in the category of Gevrey functions and ultradistributions of the complex \(\mathrm{d}^{\prime }\) naturally induced by the de Rham complex. We prove that the so-called condition \(Y(q)\) on the signature of the Levi form, for local solvability of \(\mathrm{d}^{\prime }u=f\) , is still necessary even if we take \(f\) in the classes of Gevrey functions and look for solutions \(u\) in the corresponding spaces of ultradistributions.
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