Results 31 to 40 of about 837 (138)
On a class of ultradifferentiable functions
Novi Sad Journal of Mathematics, 2015 Summary: We introduce a class of ultradifferentiable functions which contains Gevrey functions and study its basic properties. In particular, we investigate the continuity properties of certain (ultra)differentiable operators. Finally, we discuss microlocal properties in appropriate dual spaces.
Pilipović, Stevan +2 more
openaire +1 more source
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
wiley +1 more source
A non-linear theory of infrahyperfunctions [PDF]
, 2019 We develop a nonlinear theory for infrahyperfunctions (also referred to as quasianalytic (ultra)distributions by L. H\"{o}rmander). In the hyperfunction case our work can be summarized as follows.
Debrouwere, Andreas +2 more
core +2 more sources
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
wiley +1 more source
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
wiley +1 more source
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
wiley +1 more source
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
wiley +1 more source
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
wiley +1 more source
Almost analytic extensions of ultradifferentiable functions with applications to microlocal analysis
, 2019 We review and extend the description of ultradifferentiable functions by their almost analytic extensions, i.e., extensions to the complex domain with specific vanishing rate of the $\bar \partial$-derivative near the real domain.
Fürdös, Stefan +3 more
core +1 more source
Discrete characterizations of wave front sets of Fourier-Lebesgue and quasianalytic type [PDF]
, 2016 We obtain discrete characterizations of wave front sets of Fourier-Lebesgue and quasianalytic type. It is shown that the microlocal properties of an ultradistribution can be obtained by sampling the Fourier transforms of its localizations over a lattice ...
Debrouwere, Andreas, Vindas, Jasson
core +2 more sources