Formal \(P\)-Gevrey series solutions of first order holomorphic PDEs

Formal \(P\)-Gevrey series solutions of first order holomorphic PDEs

We provide a complete and self-contained proof of the Gevrey character, in an analytic function \(P\), of formal power series solutions of some families of first order holomorphic PDEs. Our approach is based on a majorant series technique by applying Nagumo norms joint with a division algorithm.

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Veröffentlicht in:arXiv.org 2022-01
Hauptverfasser: Carrillo, Sergio A, Hurtado, Carlos A
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Analytic functions
Mathematical analysis
Norms
Power series
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Zusammenfassung:We provide a complete and self-contained proof of the Gevrey character, in an analytic function \(P\), of formal power series solutions of some families of first order holomorphic PDEs. Our approach is based on a majorant series technique by applying Nagumo norms joint with a division algorithm.
ISSN:2331-8422