Negative results on the Nash-Moser theorem for Köthe sequence spaces and for spaces of ultradifferentiable functions

DOI10.1007/BF02568319zbMath0871.46003MaRDI QIDQ1352993

Markus Poppenberg

Publication date: 20 February 1997

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/156206

zbMATH Keywords

counterexampleGevrey classesNash-Moser inverse function theoremKöthe sequence spacesspaces of ultradifferentiable functions of Beurling type

Mathematics Subject Classification ID

Sequence spaces (including Köthe sequence spaces) (46A45) Topological linear spaces of continuous, differentiable or analytic functions (46E10) Topological linear spaces of test functions, distributions and ultradistributions (46F05) Derivatives of functions in infinite-dimensional spaces (46G05)

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Cites Work

• The imbedding problem for Riemannian manifolds
• A simple Nash-Moser implicit function theorem
• Bases in spaces of ultradifferentiable functions with compact support
• On E. Borel's theorem
• An inverse function theorem in Frechet-spaces
• Ein Isomorphiesatz für Potenzreihenräume
• The boundary problems of physical geodesy
• Charakterisierung der Unterräume von \((s)\)
• Die Nuklearität der Ultradistributionsräume und der Satz vom Kern. I
• Die Nuklearität der Ultradistributionsräume und der Satz vom Kern. II
• Ultradifferentiable functions and Fourier analysis
• Whitney's extension theorem for ultradifferentiable functions of Beurling type
• A tame splitting theorem for exact sequences of Fréchet spaces
• An inverse function theorem for Fréchet spaces admitting generalized smoothing operators
• Ultradifferentiable Functions on Compact Intervals
• Power Series Space Representations of Nuclear Frechet Spaces
• A NEW TECHNIQUE FOR THE CONSTRUCTION OF SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS
• Linear Extension Operators for Ultradifferentiable Functions of Beurling Type on Compact Sets
• A Decomposition Lemma for Entire Functions and its Applications to Spaces of Ultradifferentiable Functions
• On the Nash-Moser implicit function theorem
• Charakterisierung der Quotientenräume von s und eine Vermutung von Martineau
• The inverse function theorem of Nash and Moser
• Extension of C ∞ Functions Defined in a Half Space
• On Nash's implicit functional theorem
• Un théorème de fonctions implicites sur certains espaces de Fréchet et quelques applications
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