Results 71 to 80 of about 108 (94)
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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, 1986Let \({\mathcal E}_ A(L)\) 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, 2011The 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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On the Moment Problem in the Spaces of Ultradifferentiable Functions of Mean Type
Siberian Mathematical Journal, 2022The 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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Almost holomorphic extensions of ultradifferentiable functions
Journal d'Analyse Mathématique, 2003For 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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Invariant Subspaces in Nonquasianalytic Spaces of Ω-Ultradifferentiable Functions on an Interval
Russian Mathematics, 2023In this paper we consider a weakened version of the spectral synthesis for the differentiation operator in nonquasianalytic spaces of ultradifferentiable functions. We deal with the widest possible class of spaces of ultradifferentiable functions among all known ones.
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Mathematische Nachrichten, 1989
Let \(K\subset {\mathbb{R}}^ n\) be a compact set with \(\overset \circ K\neq \emptyset\) which is of the form \(K=\prod^{m}_{j=1}\bar G_ j\) where \(G_ j\subset {\mathbb{R}}^{n_ j}\), \(1\leq n_ j\leq n\), is a bounded open set with real-analytic boundary.
Meise, Reinhold, Taylor, B. Alan
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Let \(K\subset {\mathbb{R}}^ n\) be a compact set with \(\overset \circ K\neq \emptyset\) which is of the form \(K=\prod^{m}_{j=1}\bar G_ j\) where \(G_ j\subset {\mathbb{R}}^{n_ j}\), \(1\leq n_ j\leq n\), is a bounded open set with real-analytic boundary.
Meise, Reinhold, Taylor, B. Alan
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On Borel’s theorem for spaces of ultradifferentiable functions of mean type
Results in Mathematics, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Roots in differential rings of ultradifferentiable functions
Analysis Mathematica, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Continuous Linear Extension of Ultradifferentiable Functions of Beurling Type
Mathematische Nachrichten, 1993AbstractFor a weight function ω and a closed set A ⊂ ℝN let ℰ(ω)(A) denote the space of all ω‐Whitney jets of Beurling type on A. It is shown that for each closed set A ⊂ ℝN there exists an ω‐extension operator EA: ℰ(ω)(A) → ℰ(ω)(ℝN) if and only if ω is a (DN)‐function (see MEISE and TAYLOR [18], 3.3).
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