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Extension maps in ultradifferentiable and ultraholomorphic function spaces

Jean Schmets, Manuel Valdivia (2000)

Studia Mathematica

The problem of the existence of extension maps from 0 to ℝ in the setting of the classical ultradifferentiable function spaces has been solved by Petzsche [9] by proving a generalization of the Borel and Mityagin theorems for $C^{\infty}$ -spaces. We get a Ritt type improvement, i.e. from 0 to sectors of the Riemann surface of the function log for spaces of ultraholomorphic functions, by first establishing a generalization to some nonclassical ultradifferentiable function spaces.

Extension of Analytic Functional Calculus Mappings and Duality by ...-Closed Forms with Growth.

Bernd Droste (1982)

Mathematische Annalen

Extension of Continuous Functionals

Eugen Futáš (1971)

Matematický časopis

Extension of CR functions to «wedge type» domains

Andrea D'Agnolo, Piero D'Ancona, Giuseppe Zampieri (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let $X$ be a complex manifold, $S$ a generic submanifold of $X^{R}$ , the real underlying manifold to $X$ . Let $Ω$ be an open subset of $S$ with $\partial Ω$ analytic, $Y$ a complexification of $S$ . We first recall the notion of $Ω$ -tuboid of $X$ and of $Y$ and then give a relation between; we then give the corresponding result in terms of microfunctions at the boundary. We relate the regularity at the boundary for ${\bar{\partial}}_{b}$ to the extendability of $C R$ functions on $Ω$ to $Ω$ -tuboids of $X$ . Next, if $X$ has complex dimension 2, we give results on extension...

Extension of distributions and representation by derivatives of continuous functions.

Jérôme Lemoine, Jacques Simon (1996)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

It is proved that any Banach valued distribution on a bounded set can be extended to all of $R^{d}$ if and only if it is a derivative of a uniformly continuous function. A similar result is given for distributions on an unbounded set. An example shows that this does not extend to Frechet valued distributions. This relies on the fact that a Banach valued distribution is locally a derivative of a uniformly continuous function. For sake of completeness, a global representation of a Banach valued distribution...

Extension of ultradifferentiable functions.

Michael Langenbruch (1994)

Manuscripta mathematica

Extensions de jets dans des intersections de classes non quasi-analytiques

P. Beaugendre (2001)

Annales Polonici Mathematici

In [3], J. Chaumat and A.-M. Chollet prove, among other things, a Whitney extension theorem, for jets on a compact subset E of ℝⁿ, in the case of intersections of non-quasi-analytic classes with moderate growth and a Łojasiewicz theorem in the regular situation. These intersections are included in the intersection of Gevrey classes. Here we prove an extension theorem in the case of more general intersections such that every $C^{\infty}$ -Whitney jet belongs to one of them. We also prove a linear extension theorem...

Extensions of Integral Operators.

Pawel Szeptycki, Iwo Labuda (1988)

Mathematische Annalen

Extensions of two theorems on the neutrix convolution product of distributions

Brian Fisher (1991)

Annales Polonici Mathematici

Displaying 21 – 29 of 29

Currently displaying 21 – 29 of 29