Results 21 to 30 of about 837 (138)
Iterates of systems of operators in spaces of $\omega $-ultradifferentiable functions [PDF]
Annales Polonici Mathematici, 2016 Given two systems $P=(P_j(D))_{j=1}^N$ and $Q=(Q_j(D))_{j=1}^M$ of linear partial differential operators with constant coefficients, we consider the spaces ${\mathcal E}_ω^P$ and ${\mathcal E}_ω^Q$ of $ω$-ultradifferentiable functions with respect to the iterates of the systems $P$ and $Q$ respectively.
Chiara Boiti +2 more
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On Kernels of Convolution Operators in the Roumieu Spaces of Ultradifferentiable Functions
Владикавказский математический журналВ работе исследуются операторы свертки в пространствах Румье ультрадифференцируемых функций нормального типа на числовой прямой. К данному классу пространств относятся известные классы Жевре. В качестве частных случаев операторы свертки включают в себя дифференциальные операторы бесконечного порядка с постоянными коэффициентами, дифференциально ...
Daria Poliakova
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Functions with Ultradifferentiable Powers [PDF]
Results in Mathematics, 2020 We study the regularity of smooth functions $f$ defined on an open set of $\mathbb{R}^n$ and such that, for certain integers $p\geq 2$, the powers $f^p :x\mapsto (f(x))^p$ belong to a Denjoy-Carleman class $\mathcal{C}_M$ associated with a suitable weight sequence $M$. Our main result is a statement analogous to a classic theorem of H.
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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.
Vincent Thilliez
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Universality and ultradifferentiable functions: Fekete’s theorem [PDF]
Proceedings of the American Mathematical Society, 2010 The purpose of this article is to establish extensions of Fekete’s Theorem concerning the existence of universal power series of C
Mouze, Augustin, Nestoridis, V.
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Paley-Wiener-type theorem for polynomial ultradifferentiable functions
Karpatsʹkì Matematičnì Publìkacìï, 2015 The image of the space of ultradifferentiable functions with compact supports under Fourier-Laplace transformation is described. An analogue of Paley-Wiener theorem for polynomial ultradifferentiable functions is proved.
S.V. Sharyn
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Karpatsʹkì Matematičnì Publìkacìï, 2013 The representation of convolution Gevrey algebra of ultradistributions as commutant of the $n$-parametric strongly continuous semigroup of shifts in algebra of linear and continuous mappings over the space of ultradifferentiable Gevrey functions with ...
A. V. Solomko
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Rotation invariant ultradistributions [PDF]
, 2017 We prove that an ultradistribution is rotation invariant if and only if it coincides with its spherical mean. For it, we study the problem of spherical representations of ultradistributions on $\mathbb{R}^{n}$. Our results apply to both the quasianalytic
Vindas Diaz, Jasson, Vuckovic, Dorde
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A note on the barrelledness of weighted PLB-spaces of ultradifferentiable functions
Zeitschrift für Analysis und ihre Anwendungen, 2023 In this note, we consider weighted PLB-spaces of ultradifferentiable functions defined via a weight function and a weight system, as introduced in our previous work (2022). We provide a complete characterization of when these spaces are ultrabornological and barrelled in terms of the defining weight system, thereby improving the ...
Andreas Debrouwere, Lenny Neyt
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Application of the functional calculus to solving of infinite dimensional heat equation
Karpatsʹkì Matematičnì Publìkacìï, 2016 In this paper we study infinite dimensional heat equation associated with the Gross Laplacian. Using the functional calculus method, we obtain the solution of appropriate Cauchy problem in the space of polynomial ultradifferentiable functions.
S.V. Sharyn
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