Results 11 to 20 of about 108 (94)
Polynomials on the space of ω-ultradifferentiable functions [PDF]
Opuscula Mathematica, 2007 The space of polynomials on the the space \(D_{\omega}\) of \(\omega\)-ultradifferentiable functions is represented as the direct sum of completions of symmetric tensor powers of \(D^{\prime}_{\omega}\).
Katarzyna Grasela
doaj +2 more sources
Ultradifferentiable classes of entire functions. [PDF]
Adv Oper Theory, 2023 AbstractWe study classes of ultradifferentiable functions defined in terms of small weight sequences violating standard growth and regularity requirements. First, we show that such classes can be viewed as weighted spaces of entire functions for which the crucial weight is given by the associated weight function of the so-called conjugate weight ...
Nenning DN, Schindl G.
europepmc +5 more sources
The overdetermined Cauchy problem for $$\omega $$ ω -ultradifferentiable functions [PDF]
manuscripta mathematica, 2017 In this paper we study the Cauchy problem for overdetermined systems of linear partial differential operators with constant coefficients in some spaces of $\omega$-ultradifferentiable functions in the sense of Braun, Meise and Taylor, for non-quasianalytic weight functions $\omega$.
BOITI, Chiara, Elisabetta Gallucci
openaire +7 more sources
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.
openaire +3 more sources
On the conjugate weight function and ultradifferentiable classes of entire functions. [PDF]
Adv Oper TheoryAbstract We introduce the new notion of a conjugate weight function and provide a detailed study of this operation and its properties. Then we apply this knowledge to study classes of ultradifferentiable functions defined in terms of fast growing weight functions in the sense of Braun–Meise–Taylor and hence violating standard ...
Schindl G.
europepmc +3 more sources
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
openaire +8 more sources
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.
openaire +1 more source
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
openaire +2 more sources
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
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