Whitney's extension theorem for non-quasi-analytic classes of ultradifferentiable functions.

José Bonet; Rüdiger W. Braun; Reinhold Meise; B. A. Taylor

Displaying similar documents to “Whitney's extension theorem for non-quasi-analytic classes of ultradifferentiable functions.”

Whitney's extension theorem for nonquasianalytic classes of ultradifferentiable functions

J. Bonet, R. Braun, R. Meise, B. Taylor (1991)

Studia Mathematica

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On the range of convolution operators on non-quasianalytic ultradifferentiable functions

Jóse Bonet, Antonio Galbis, R. Meise (1997)

Studia Mathematica

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Let $ℇ_{(ω)} (Ω)$ denote the non-quasianalytic class of Beurling type on an open set Ω in $ℝ^{n}$ . For $μ \in ℇ_{(ω)}^{'} (ℝ^{n})$ the surjectivity of the convolution operator $T_{μ} : ℇ_{(ω)} (Ω_{1}) \to ℇ_{(ω)} (Ω_{2})$ is characterized by various conditions, e.g. in terms of a convexity property of the pair $(Ω_{1}, Ω_{2})$ and the existence of a fundamental solution for μ or equivalently by a slowly decreasing condition for the Fourier-Laplace transform of μ. Similar conditions characterize the surjectivity of a convolution operator $S_{μ} : D_{ω}^{'} (Ω_{1}) \to D_{ω}^{'} (Ω_{2})$ between ultradistributions of Roumieu type whenever...

A general approximation theorem of Whitney type.

Michael Langenbruch (2003)

RACSAM

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We show that Whitney?s approximation theorem holds in a general setting including spaces of (ultra)differentiable functions and ultradistributions. This is used to obtain real analytic modifications for differentiable functions including optimal estimates. Finally, a surjectivity criterion for continuous linear operators between Fréchet sheaves is deduced, which can be applied to the boundary value problem for holomorphic functions and to convolution operators in spaces of ultradifferentiable...

Splitting of the ∂-complex in weighted spaces of square integrable functions.

Michael Langenbruch (1992)

Revista Matemática de la Universidad Complutense de Madrid

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Sequence space representations for zero-solutions of convolution equations on ultradifferentiable functions of Roumieu type

Reinhold Meise (1989)

Studia Mathematica

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A sequence space representation of the space of bounded ultradistributions of Beurling type.

María del Carmen Gómez-Collado (2002)

RACSAM

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Sequence space representations of the spaces D(R) and of its dual D'(R), the space of bounded ultradistributions of Beurling type, are presented, in case the weight ω is a strong weight.

Associated weights and spaces of holomorphic functions

Klaus Bierstedt, José Bonet, Jari Taskinen (1998)

Studia Mathematica

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When treating spaces of holomorphic functions with growth conditions, one is led to introduce associated weights. In our main theorem we characterize, in terms of the sequence of associated weights, several properties of weighted (LB)-spaces of holomorphic functions on an open subset $G \subset ℂ^{N}$ which play an important role in the projective description problem. A number of relevant examples are provided, and a “new projective description problem” is posed. The proof of our main result can also...

Sequence space representations for (FN)-algebras of entire functions modulo closed ideals

Reinhold Meise, B. Taylor (1987)

Studia Mathematica

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Weighted estimates for differential operators with operator-valued coefficients

W.O. Amrein, A. M. Boutet de Monvel-Berthier, V. Georgescu (1987)

Bulletin de la Société Mathématique de France

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