Results 41 to 50 of about 146 (115)
Extension of Functions with ω-Rapid Polynomial Approximation [PDF]
, 1995 For a weight function ω : [0, ∞[ → [0, ∞[ we denote by E(ω)(RN) the class of all ω-ultradifferentiable functions of Beurling type on RN. Each element in E(ω)(RN) is a function with ω-rapid polynomial approximation on each compact set K ⊂ of RN, whenever ...
Franken, U.
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International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 45, Page 2401-2422, 2004., 2004 Necessary and sufficient conditions for a scalar type spectral operator in a Banach space to be a generator of an infinite differentiable or a Gevrey ultradifferentiable C0‐semigroup are found, the latter formulated exclusively in terms of the operator′s spectrum.
Marat V. Markin
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On the Carleman classes of vectors of a scalar type spectral operator
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 60, Page 3219-3235, 2004., 2004 The Carleman classes of a scalar type spectral operator in a reflexive Banach space are characterized in terms of the operator′s resolution of the identity. A theorem of the Paley‐Wiener type is considered as an application.
Marat V. Markin
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A note on the spectral operators of scalar type and semigroups of bounded linear operators
International Journal of Mathematics and Mathematical Sciences, Volume 32, Issue 10, Page 635-640, 2002., 2002 It is shown that, for the spectral operators of scalar type, the well‐known characterizations of the generation of C0‐ and analytic semigroups of bounded linear operators can be reformulated exclusively in terms of the spectrum of such operators, the conditions on the resolvent of the generator being automatically met and the corresponding semigroup ...
Marat V. Markin
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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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On the Theorem of Borel for Quasianalytic Classes [PDF]
, 2013 We investigate the surjectivity of the Borel map in the quasianalytic setting for classes of ultradifferentiable functions defined in terms of the growth of the Fourier-Laplace transform.
Bonet, José, Meise, Reinhold
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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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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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On the Stability of Analytic Germs under Ultradifferentiable Perturbations [PDF]
, 2007 AMS-LaTeX, 10 pagesInternational audienceLet $ f$ be a real-analytic function germ whose critical locus contains a given real-analytic set $ X $, and let $ Y $ be a germ of closed subset of $ \mathbb{R}^n $ at the origin.
Thilliez, Vincent
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