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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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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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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Global ultradifferentiable functions and applications [PDF]
, 2019 The class of global Gevrey functions was introduced recently by Z. Adwan, G. Hoepfner and A. Raich, the elements in these spaces are defined in terms of its derivatives with estimates that depend on sequences.
Rampazo, Patrícia Yukari Sato
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Ultrarapidly decreasing ultradifferentiable functions, Wigner distributions and density matrices [PDF]
, 2008 International audienceSpaces S(omega), S{(omega) over bar}, S((omega) over bar) of ultradecreasing ultradifferentiable (or for short, ultra-S) functions, depending on a weight e(omega(x)), are introduced in the context of quantum statistics.
Jean-Marie Aubry, Aubry, Jean-Marie
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Regularity of global solutions of partial differential equations in non isotropic ultradifferentiable spaces via time-frequency methods [PDF]
, 2021 In this paper we study regularity of partial differential equations with polynomial coefficients in non isotropic Beurling spaces of ultradifferentiable functions of global type.
Alessandro Oliaro, Claudio Mele
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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 +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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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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