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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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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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Superposition in Classes of Ultradifferentiable Functions
Publications of the Research Institute for Mathematical Sciences, 2006 We present a complete characterization of the classes of ultradifferentiable functions that are holomorphically closed. Moreover, we show that any class holomorphically closed is also closed under composition (now without restrictions on the number of variables).
Fernández, Carmen, Galbis, Antonio
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, 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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Unified Treatment of the Krätzel Transformation for Generalized Functions
Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013 We discuss a generalization of the Krätzel transforms on certain spaces of ultradistributions. We have proved that the Krätzel transform of an ultradifferentiable function is an ultradifferentiable function and satisfies its Parseval′s inequality. We also provide a complete reading of the transform constructing two desired spaces of Boehmians.
S. K. Q. Al-Omari +2 more
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Abstract and Applied Analysis, Volume 2012, Issue 1, 2012., 2012 We study a q‐analog of a singularly perturbed Cauchy problem with irregular singularity in the complex domain which generalizes a previous result by Malek in (2011). First, we construct solutions defined in open q‐spirals to the origin. By means of a q‐Gevrey version of Malgrange‐Sibuya theorem we show the existence of a formal power series in the ...
Alberto Lastra +2 more
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Inégalité de Markov en plusieurs variables
International Journal of Mathematics and Mathematical Sciences, Volume 2006, Issue 1, 2006., 2006 L′inégalité de Markov joue un rôle important en théorie constructive de fonctions. Dans les deux dernières décennies, on a développé sa théorie multidimensionnelle. Le but de cet article est de présenter le récent progrès de cette belle théorie.Markov′s inequality plays an important role in constructive function theory.
Wiesław Pleśniak
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International Journal of Mathematics and Mathematical Sciences, Volume 2006, Issue 1, 2006., 2006 The tempered ultradistribution space of Roumieu type for the space Hμ,ν is defined, which is a subspace of the Hausdörff locally convex topological linear space. Further, results are obtained for the multipliers and operators on the tempered ultradistribution spaces for the distributional Hankel‐type transformation spaces.
P. K. Banerji, S. K. Al-Omari
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Gelfand–Shilov Spaces for Extended Gevrey Regularity
AxiomsWe consider spaces of smooth functions obtained by relaxing Gevrey-type regularity and decay conditions. It is shown that these classes can be introduced by using the general framework of the weighted matrices approach to ultradifferentiable functions ...
Nenad Teofanov +2 more
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Asymptotic hyperfunctions, tempered hyperfunctions, and asymptotic expansions
International Journal of Mathematics and Mathematical Sciences, Volume 2005, Issue 5, Page 755-788, 2005., 2005 We introduce new subclasses of Fourier hyperfunctions of mixed type, satisfying polynomial growth conditions at infinity, and develop their sheaf and duality theory. We use Fourier transformation and duality to examine relations of these asymptotic and tempered hyperfunctions to known classes of test functions and distributions, especially the Gel′fand‐
Andreas U. Schmidt
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