Results 31 to 40 of about 108 (94)
Division by Flat Ultradifferentiable Functions and Sectorial Extensions [PDF]
Results in Mathematics, 2003 We consider classes $ \mathcal{A}_M(S) $ of functions holomorphic in an open plane sector $ S $ and belonging to a strongly non-quasianalytic class on the closure of $ S $. In $ \mathcal{A}_M(S) $, we construct functions which are flat at the vertex of $ S $ with a sharp rate of vanishing.
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Mathematische Nachrichten, Volume 298, Issue 2, Page 456-477, February 2025.Abstract We give a simple construction of the log‐convex minorant of a sequence {Mα}α∈N0d$\lbrace M_\alpha \rbrace _{\alpha \in \mathbb {N}_0^d}$ and consequently extend to the d$d$‐dimensional case the well‐known formula that relates a log‐convex sequence {Mp}p∈N0$\lbrace M_p\rbrace _{p\in \mathbb {N}_0}$ to its associated function ωM$\omega _M$, that
Chiara Boiti +3 more
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About spaces of $\omega_1$-$\omega_2$-ultradifferentiable functions
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2008 Nonisotropic spaces of ultradifferentiable functions are introduced on products \( \Omega_1 \times \Omega_2 \subset \mathbb R^r \times \mathbb R^s \) in such a way that the first \(r\) partial derivatives are governed by a weight function \( \omega_1 \) in the sense of \textit{R.\,W.\thinspace Braun, R.\,Meise} and \textit{B.\,A.\thinspace Taylor ...
Schmets, Jean, Valdivia, Manuel
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The Metivier inequality and ultradifferentiable hypoellipticity
Mathematische Nachrichten, Volume 297, Issue 7, Page 2517-2531, July 2024.Abstract In 1980, Métivier characterized the analytic (and Gevrey) hypoellipticity of L2$L^2$‐solvable partial linear differential operators by a priori estimates. In this note, we extend this characterization to ultradifferentiable hypoellipticity with respect to Denjoy–Carleman classes given by suitable weight sequences. We also discuss the case when
Paulo D. Cordaro, Stefan Fürdös
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Extension of ultradifferentiable functions
Manuscripta Mathematica, 1994 The extension problem considered in this paper is of the type given below: Let \(K_1\) and \(K\) be compact convex sets such that \(\text{int} (K_1) \supset K\), and such that \(\text{int} (K)\neq \emptyset\) or \(K= \{0\}\) and let a sequence \((N_a)\) of positive numbers be given.
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An Introduction to Extended Gevrey Regularity
AxiomsGevrey classes are the most common choice when considering the regularities of smooth functions that are not analytic. However, in various situations, it is important to consider smoothness properties that go beyond Gevrey regularity, for example, when ...
Nenad Teofanov +2 more
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On ultradifferentiable functions
, 2016 25 pages. Withdrawn and superseded by an extended version with the title "On the Siegel-Sternberg linearization theorem:"
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A correction to “Ultradifferentiable functions on lines in ℝⁿ" [PDF]
Proceedings of the American Mathematical Society, 2002 The proof of Theorem 1 in Proc. Amer. Math. Soc. 127 (1999), no. 7, 2099–2104, is revised.
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Whitney’s extension theorem for ultradifferentiable functions of Beurling type
Arkiv för Matematik, 1988 The authors introduce classes of non-quasianalytic functions \({\mathcal E}_{\omega}({\mathbb{R}}^ n)\) similar to those treated by Beurling and Björck: Given a weight function \(\omega\) : \({\mathbb{R}}\to [0,\infty [\) (i.e. \(\omega\) is continuous, even, increasing on [0,\(\infty [\), satisfies \(\omega (0)=0\), lim \(\omega\) (t)\(=\infty ...
Meise, Reinhold, Taylor, B. Alan
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On invertibility of Duhamel operator in spaces of ultradifferentiable functions
Ufa Mathematical Journal, 2023 Summary: Let \(\Delta\) be a non-point segment or an (open) interval on the real line containing the point 0. In the space of entire functions realized by the Fourier-Laplace transform of the dual space to the space of ultradifferentiable or of all infinitely differentiable functions on \(\Delta \), we study the operators from the commutator subgroup ...
Olga Aleksandrovna Ivanova +1 more
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