Results 111 to 120 of about 837 (138)

Continuation of functionals on ultradifferentiable function spaces

Analysis Mathematica, 1995
The paper generalizes a few results of \textit{M. A. Solov'ev} [Theor. Math. Phys. 15, 317-328 (1974; Zbl 0273.46030)] and adds further results in line with the first author's work on the subject. The Fourier-Laplace transform of functionals defined on the spaces \(Sa^q_k\) are considered. It may be mentioned here that \textit{J. M. C.
Pathak, R. S., Paul, A. C.
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Holomorphic approximation of ultradifferentiable functions

Mathematische Annalen, 1981
Introduct ion Let S be a closed subset of some open set in Cn and denote by dT(S) the space of germs of holomorphic functions on (a neighborhood of) S. For a space F(S) of tEvalued (continuous, differentiable etc.) functions on S [containing t~(S)] the problem of holomorphic approximation consists of finding conditions to ensure that the natural ...
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Ultradifferentiable Functions on Compact Intervals

Mathematische Nachrichten, 1989
The author deals with finding the spaces of ultradifferentiable functions which are linear topologically isomorphic to a power series space. The problem is treated for the spaces \({\mathcal E}_{(M_ p)}(I)\) (and \({\mathcal E}_{\{M_ p\}}(I))\) of all ultradifferentiable functions of the Beurling type (resp.
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Ultradifferentiable functions and Fourier analysis

Results in Mathematics, 1990
In Beurling's approach to ultradifferentiable functions, decay properties of the Fourier transform of the functions are imposed rather than growth conditions on the derivatives, as it has been done classically. In the present article the authors modify Beurling's approach. They define for nonempty open subsets \(\Omega\) of \(\mathbb{R}^ N\) the spaces
Braun, R. W., Meise, R., Taylor, B. A.
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Extension of ultradifferentiable functions of Roumieu type

Archiv Der Mathematik, 1988
Let \(K\subset {\mathbb{R}}^ n\) be a compact convex set and let \(E_{\{M_ j\}}(K)\) denote the ultradifferentiable functions of Roumieu type on K. It is shown, that there is no continuous linear extension operator \(T: E_{\{M_ j\}}(K)\to E_{\{M_ j\}}(J)\), if the sequence \((M_ j)\) is regular (\(K\subset\overset\circ J\subset {\mathbb{R}}^ n)\). This
Michael langenbruch
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Weight functions for classes of ultradifferentiable functions

Results in Mathematics, 1994
\textit{A. Beurling} [Lectures 4 and 5, AMS Summer Institute, Stanford (1961)] has used subadditive weight functions \(\omega\) to define non- quasianalytic classes of ultradifferentiable functions \({\mathcal E}_{(\omega)} (\mathbb{R})\). Some authors also have defined different weight functions for the classes \({\mathcal E}_{(\omega)} (\mathbb{R})\).
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Convolution equations and spaces of ultradifferentiable functions

Israel Journal of Mathematics, 1986
Let \({\mathcal E}_ A(L)\) be the topological vector space of \(C^{\infty}\) functions on \({\mathbb{R}}^ n\) which are approximate solutions to a given convolution equation \(L*f=0\), \(L\in {\mathcal E}'({\mathbb{R}}^ n)\), as in \textit{C. A. Berenstein} and \textit{M. A.
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On Whitney’s extension theorem for ultradifferentiable functions

Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 2011
The author considers ultradistributions and ultradifferentiable functions of Beurling and of Roumieu type in the sense of Komatsu, assuming on the sequence of positive numbers \((M_n)_n\) the conditions of \(M_0=1\), logarithmic convexity, stability for ultradifferentiable operators and non strong quasi-analyticity. For a nonempty open subset \(\Omega\)
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Almost holomorphic extensions of ultradifferentiable functions

Journal d'Analyse Mathématique, 2003
For a function \(f\) on the real line (or the unit circle), the existence of extension to the complex \(F\) such that \(\overline\partial F\) tends to zero in a prescribed manner when approaching the real line (respectively the unit circle) (this \(F\) is called an almost holomorphic extensions) is related to regularity properties of the function \(f\).
Andersson, Mats, Berndtsson, Bo
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On the Moment Problem in the Spaces of Ultradifferentiable Functions of Mean Type

Siberian Mathematical Journal, 2022
The author studies the image of the Borel map \[ \rho:C^\infty(\mathbb{R}) \rightarrow \mathbb{C}^\mathbb{N}, \quad f \mapsto (f^{(n)}(0))_n \] restricted to spaces of ultradifferentiable functions of mean type as introduced in [\textit{D. A. Abanina}, Result. Math. 44, No. 3--4, 195--213 (2003; Zbl 1057.46025)].
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