Results 1 to 10 of about 105 (96)
Ultradifferentiable classes of entire functions. [PDF]
Adv Oper Theory, 2023 AbstractWe study classes of ultradifferentiable functions defined in terms of small weight sequences violating standard growth and regularity requirements. First, we show that such classes can be viewed as weighted spaces of entire functions for which the crucial weight is given by the associated weight function of the so-called conjugate weight ...
Nenning DN, Schindl G.
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International Journal of Mathematics and Mathematical Sciences, 2018 Let Sω′(R) be the space of tempered distributions of Beurling type with test function space Sω(R) and let Eω,p be the space of ultradifferentiable functions with arbitrary support having a period p. We show that Eω,p is generated by Sω(R).
Byung Keun Sohn
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Nuclear global spaces of ultradifferentiable functions in the matrix weighted setting. [PDF]
Banach J Math Anal, 2021 AbstractWe prove that the Hermite functions are an absolute Schauder basis for many global weighted spaces of ultradifferentiable functions in the matrix weighted setting and we determine also the corresponding coefficient spaces, thus extending the previous work by Langenbruch.
Boiti C, Jornet D, Oliaro A, Schindl G.
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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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Polynomials on the space of ω-ultradifferentiable functions [PDF]
Opuscula Mathematica, 2007 The space of polynomials on the the space \(D_{\omega}\) of \(\omega\)-ultradifferentiable functions is represented as the direct sum of completions of symmetric tensor powers of \(D^{\prime}_{\omega}\).
Katarzyna Grasela
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The overdetermined Cauchy problem for $$\omega $$ ω -ultradifferentiable functions [PDF]
manuscripta mathematica, 2017 In this paper we study the Cauchy problem for overdetermined systems of linear partial differential operators with constant coefficients in some spaces of $\omega$-ultradifferentiable functions in the sense of Braun, Meise and Taylor, for non-quasianalytic weight functions $\omega$.
BOITI, Chiara, Elisabetta Gallucci
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Extended Gevrey Regularity via Weight Matrices
Axioms, 2022 The main aim of this paper is to compare two recent approaches for investigating the interspace between the union of Gevrey spaces Gt(U) and the space of smooth functions C∞(U). The first approach in the style of Komatsu is based on the properties of two
Nenad Teofanov, Filip Tomić
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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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Weighted (PLB)-spaces of ultradifferentiable functions and multiplier spaces [PDF]
Monatshefte für Mathematik, 2022 We study weighted $(PLB)$-spaces of ultradifferentiable functions defined via a weight function (in the sense of Braun, Meise and Taylor) and a weight system. We characterize when such spaces are ultrabornological in terms of the defining weight system. This generalizes Grothendieck's classical result that the space $\mathcal{O}_M$ of slowly increasing
Debrouwere, Andreas, Neyt, Lenny
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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, that is, the existence of a formal real power series such that, for every \(h \in C\big([-1,1]\big)\) with \(h(0)=0\), there exists an increasing sequence \((\lambda_n) \subseteq \mathbb{N}\) such that \[ \sup_{x \in [-1,1]} \left| \sum_{k=1}^{\lambda_n} a_k x^k - h(x) \right| \
Mouze, Augustin, Nestoridis, V.
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