Results 31 to 40 of about 276 (127)

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, D. Jornet, J. Juan-Huguet, Luigi Rodino   +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, Svetlana Mincheva-Kaminska, Henryk Hudzik   +2 more
wiley   +1 more source

Almost analytic extensions of ultradifferentiable functions with applications to microlocal analysis [PDF]

, 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.
Nenning, David Nicolas, Schindl, Gerhard, Fürdös, Stefan, Rainer, Armin   +3 more
core   +2 more sources

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, Stéphane Malek, Alexander Domoshnitsky   +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, A. Kılıçman, Mustafa Bayram   +2 more
wiley   +1 more source

The overdetermined Cauchy problem in some classes of ultradifferentiable functions [PDF]

, 2001
In this paper we study the Cauchy problem for overdetermined systems of linear partial differential operators with constant coefficients in some spaces of ultradifferentiable functions of class (M_p ). We show that evolution is equivalent to the validity
Boiti C., Nacinovich M.
core   +1 more source

On q‐Gevrey Asymptotics for Singularly Perturbed q‐Difference‐Differential Problems with an Irregular Singularity

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, Stéphane Malek, Allan C. Peterson   +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

Eigenfunction expansions of ultradifferentiable functions and ultradistributions in ℝⁿ [PDF]

, 2016
We obtain a characterization of ${\mathcal S}^{\{M_p\}}_{\{M_p\}}(\mathbb{R}^n)$ and $\mathcal {S}^{(M_p)}_{(M_p)}(\mathbb{R}^n)$, the general Gelfand-Shilov spaces of ultradifferentiable functions of Roumieu and Beurling type, in terms of decay ...
Vindas Diaz, Jasson, Vuckovic, Dorde
core   +1 more source

Ultradifferentiable functions on lines in ℝⁿ [PDF]

Proceedings of the American Mathematical Society, 1999
It is well known that a function f ∈
openaire   +1 more source