An application of the Nash-Moser theorem to ordinary differential equations in Fréchet spaces

M. Poppenberg

Displaying similar documents to “An application of the Nash-Moser theorem to ordinary differential equations in Fréchet spaces”

Characterization of nuclear Fréchet spaces in which every bounded set is polar

Seán Dineen, Reinhold Meise, Dietmar Vogt (1984)

Bulletin de la Société Mathématique de France

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Complemented subspaces in tame power series spaces

Ed Dubinsky, Dietmar Vogt (1989)

Studia Mathematica

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Structure theory of power series spaces of infinite type.

Dietmar Vogt (2003)

RACSAM

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The paper gives a complete characterization of the subspaces, quotients and complemented subspaces of a stable power series space of infinite type without the assumption of nuclearity, so extending previous work of M. J. Wagner and the author to the nonnuclear case. Various sufficient conditions for the existence of bases in complemented subspaces of infinite type power series spaces are also extended to the nonnuclear case.

Generalized Nash-Moser smoothing operators and the structure of Fréchet spaces

Vincenzo Moscatelli, Marilda Simões (1987)

Studia Mathematica

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Construction of standard exact sequences of power series spaces

Markus Poppenberg, Dietmar Vogt (1995)

Studia Mathematica

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The following result is proved: Let $Λ_{R}^{p} (α)$ denote a power series space of infinite or of finite type, and equip $Λ_{R}^{p} (α)$ with its canonical fundamental system of norms, R ∈ 0,∞, 1 ≤ p < ∞. Then a tamely exact sequence (⁎) $0 \to Λ_{R}^{p} (α) \to Λ_{R}^{p} (α) \to Λ_{R}^{p} {(α)}^{ℕ} \to 0$ exists iff α is strongly stable, i.e. $l i m_{n} α_{2 n} / α_{n} = 1$ , and a linear-tamely exact sequence (*) exists iff α is uniformly stable, i.e. there is A such that $l i m s u p_{n} α_{K n} / α_{n} \leq A < \infty$ for all K. This result extends a theorem of Vogt and Wagner which states that a topologically exact sequence (*) exists iff α is stable,...

Some normability conditions on Fréchet spaces.

Tosun Terzioglu, Dietmar Vogt (1989)

Revista Matemática de la Universidad Complutense de Madrid

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We define two new normability conditions on Fréchet spaces and announce some related results.

On the functors Ext¹(E,F) for Fréchet spaces

Dietmar Vogt (1987)

Studia Mathematica

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Tensor stable Fréchet and (DF)-spaces.

José Bonet, Juan Carlos Díaz, Jari Taskinen (1991)

Collectanea Mathematica

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In this paper we introduce and investigate classes of Fréchet and (DF)-spaces which constitute a very general frame in which the problem of topologies of Grothendieck and some related dual questions have a positive answer. Many examples of spaces in theses classes are provided, in particular spaces of sequences and functions. New counterexamples to the problems of Grothendieck are given.

Complemented subspaces with a strong finite-dimensional decomposition of nuclear Köthe spaces have a basis

Jörg Krone, Volker Walldorf (1998)

Studia Mathematica

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The following result is proved: Let E be a complemented subspace with an r-finite-dimensional decomposition of a nuclear Köthe space λ(A). Then E has a basis.

Holomorphic functions and Banach-nuclear decompositions of Fréchet spaces

Seán Dineen (1995)

Studia Mathematica

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We introduce a decomposition of holomorphic functions on Fréchet spaces which reduces to the Taylor series expansion in the case of Banach spaces and to the monomial expansion in the case of Fréchet nuclear spaces with basis. We apply this decomposition to obtain examples of Fréchet spaces E for which the τ_{ω} and τ_{δ} topologies on H(E) coincide. Our result includes, with simplified proofs, the main known results-Banach spaces with an unconditional basis and Fréchet nuclear spaces...

Nuclear spaces on a locally compact group

T. Pytlik (1974)

Studia Mathematica

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