Periodic Tempered Distributions of Beurling Type and Periodic Ultradifferentiable Functions with Arbitrary Support [PDF]
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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Paley-Wiener-type theorem for polynomial ultradifferentiable functions [PDF]
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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A note on the barrelledness of weighted PLB-spaces of ultradifferentiable functions [PDF]
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 ...
Debrouwere, Andreas, Neyt, Lenny
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Convolution equations for ultradifferentiable functions and ultradistributions [PDF]
Journal of Mathematical Analysis and Applications, 2004 For convolution operators acting on spaces of ultradistributions of Beurling type on open sets, the authors characterize the surjectivity of the operator (modulo ultrasmooth functions) in terms of a convexity condition for singular supports in the spirit of Hörmander's convexity conditions (Theorem A).
Frerick, L., Wengenroth, J.
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On the Projective Description of Spaces of Ultradifferentiable Functions of Roumieu Type [PDF]
, 2021 We provide a projective description of the space $\mathcal{E}^{\{\mathfrak{M}\}}(Ω)$ of ultradifferentiable functions of Roumieu type, where $Ω$ is an arbitrary open set in $\mathbb{R}^d$ and $\mathfrak{M}$ is a weight matrix satisfying the analogue of Komatsu's condition $(M.2)'$.
Debrouwere, Andreas +2 more
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Nuclear global spaces of ultradifferentiable functions in the matrix weighted setting. [PDF]
Banach J Math Anal, 2021 We 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 previous work by
Boiti C, Jornet D, Oliaro A, Schindl G.
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Eigenfunction expansions of ultradifferentiable functions and ultradistributions [PDF]
Transactions of the American Mathematical Society, 2016 In this paper we give a global characterisation of classes of ultradifferentiable functions and corresponding ultradistributions on a compact manifold X X
Dasgupta, Aparajita, Ruzhansky, Michael
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Equality of Ultradifferentiable Classes by Means of Indices of Mixed O-regular Variation. [PDF]
Results Math, 2022 Producción CientíficaWe characterize the equality between ultradifferentiable function classes defined in terms of abstractly given weight matrices and in terms of the corresponding matrix of associated weight functions by using new growth indices. These
Jiménez-Garrido J, Sanz J, Schindl G.
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Global Wave Front Sets in Ultradifferentiable Classes [PDF]
, 2022 [EN] We introduce a global wave front set using Weyl quantizations of pseudodifferential operators of infinite order in the ultradifferentiable setting.
Jornet Casanova, David +7 more
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Multiplication and Convolution Topological Algebras in Spaces of ω-Ultradifferentiable Functions of Beurling Type [PDF]
, 2023 We determine multiplication and convolution topological algebras for classes of ω-ultradifferentiable functions of Beurling type.
Angela A. , Albanese, Claudio, Mele
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