Results 41 to 50 of about 3,122,419 (133)
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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Quasianalytic functionals and ultradistributions as boundary values of harmonic functions [PDF]
, 2023 We study boundary values of harmonic functions in spaces of quasianalytic functionals and spaces of ultradistributions of non-quasianalytic type. As an application, we provide a new approach to H\"ormander's support theorem for quasianalytic functionals.
Vindas Diaz, Jasson +3 more
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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
wiley +1 more source
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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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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Nuclearity of rapidly decreasing ultradifferentiable functions and time-frequency analysis [PDF]
, 2019 We use techniques from time-frequency analysis to show that the space $\mathcal S_\omega$ of rapidly decreasing $\omega$-ultradifferentiable functions is nuclear for every weight function $\omega(t)=o(t)$ as $t$ tends to infinity. Moreover, we prove that,
Schindl, Gerhard +8 more
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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
doaj +1 more source
Almost analytic extensions of ultradifferentiable functions with applications to microlocal analysis [PDF]
, 2019 We review and extend the description of ultradifferentiable functions by their almost analytic extensions, i.e., extensions to the complex domain with specific vanishing rate of the $\bar \partial$-derivative near the real domain.
Nenning, David Nicolas +3 more
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Polynomials on the space of ω-ultradifferentiable functions [PDF]
, 2007 The space of polynomials on the space Dω of ω-ultradifferentiable functions is represented as the direct sum of completions of symmetric tensor powers of D′ω
Grasela, K.
core
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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