Inverse map theorem in the ultra-\(F\)-differentiable class

DOI10.3792/pjaa.65.199zbMath0759.58009OpenAlexW2008496903MaRDI QIDQ1813893

Takesi Yamanaka

Publication date: 25 June 1992

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.65.199

zbMATH Keywords

Banach spacessmooth mapinverse function theoremultra \(F\)-differentiable derivative

Mathematics Subject Classification ID

Differentiation theory (Gateaux, Fréchet, etc.) on manifolds (58C20) Implicit function theorems, Jacobians, transformations with several variables (26B10) Derivatives of functions in infinite-dimensional spaces (46G05) Implicit function theorems; global Newton methods on manifolds (58C15)

Related Items (11)

On ODEs in the ultradifferentiable class ⋮ Asymptotich-expansiveness rate ofC^∞maps ⋮ The exponential law for spaces of test functions and diffeomorphism groups ⋮ The convenient setting for quasianalytic Denjoy-Carleman differentiable mappings ⋮ The convenient setting for Denjoy-Carleman differentiable mappings of Beurling and Roumieu type ⋮ Inverse mapping theorem in the ultradifferentiable class ⋮ An exotic zoo of diffeomorphism groups on \(\mathbb {R}^n\) ⋮ On the Siegel-Sternberg linearization theorem ⋮ The Trouvé group for spaces of test functions ⋮ The Gevrey normalization for quasi-periodic systems under Siegel type small divisor conditions ⋮ Equivalence of stability properties for ultradifferentiable function classes

Cites Work

• The implicit function theorem for ultradifferentiable mappings
• A new higher order chain rule and Gevrey class

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