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Local Factorization of Differential Forms on Fréchet–Schwartz Spaces

✍ Scribed by Roberto Luiz Soraggi

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
245 KB
Volume
209
Category
Article
ISSN
0022-247X

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✦ Synopsis

The reduction of the Ѩ-problem on a Frechet nuclear space to the study of the Ѩ-operator on a Hilbert space produces a global solution u when the second member w factors globally through this Hilbert space. Easy counterexamples show that this global factorization is not in general possible and hence we can expect only local factorization of w. We show that C C pq 1 differential forms on a Frechet᎐Schwartz space factor locally through a normed space as C C p differential forms. The counterexamples deal with arbitrary C C ϱ differential forms w, while our results holds for certain C C ϱ second members, in particular for all holomorphic w. More precisely, we construct, using local solutions of Ѩ u s w due to Raboin and ϱ Ž . Colombeau and Perrot, a C C solution u: E ª C, when w is a holomorphic 0, 1 form on a Frechet nuclear space E.

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