Results 1 to 10 of about 51 (49)
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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Unified Treatment of the Krätzel Transformation for Generalized Functions
Abstract and Applied Analysis, 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.
S. K. Q. Al-Omari, A. Kılıçman
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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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Comment on “On the Carleman Classes of Vectors of a Scalar Type Spectral Operator”
International Journal of Mathematics and Mathematical Sciences, Volume 2018, Issue 1, 2018., 2018 The results of three papers, in which the author inadvertently overlooks certain deficiencies in the descriptions of the Carleman classes of vectors, in particular the Gevrey classes, of a scalar type spectral operator in a complex Banach space established in “On the Carleman Classes of Vectors of a Scalar Type Spectral Operator,” Int. J. Math.
Marat V. Markin, Yuri Latushkin
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Wave Front Sets with respect to the Iterates of an Operator with Constant Coefficients
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 We introduce the wave front set WF*P(u) with respect to the iterates of a hypoelliptic linear partial differential operator with constant coefficients of a classical distribution u ∈ 𝒟′(Ω) in an open set Ω in the setting of ultradifferentiable classes of Braun, Meise, and Taylor.
C. Boiti +3 more
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Compatibility Conditions and the Convolution of Functions and Generalized Functions
Journal of Function Spaces, Volume 2013, Issue 1, 2013., 2013 The paper is a review of certain existence theorems concerning the convolution of functions, distributions, and ultradistributions of Beurling type with supports satisfying suitable compatibility conditions. The fact that some conditions are essential for the existence of the convolution in the discussed spaces follows from earlier results and the ...
Andrzej Kamiński +2 more
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On Parametric Gevrey Asymptotics for Singularly Perturbed Partial Differential Equations with Delays
Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013 We study a family of singularly perturbed q‐difference‐differential equations in the complex domain. We provide sectorial holomorphic solutions in the perturbation parameter ϵ. Moreover, we achieve the existence of a common formal power series in ϵ which represents each actual solution and establish q‐Gevrey estimates involved in this representation ...
Alberto Lastra +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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