Results 31 to 40 of about 146 (115)
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
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Nuclearity of rapidly decreasing ultradifferentiable functions and time-frequency analysis [PDF]
, 2019 We use techniques from time-frequency analysis to show that the space $\mathcal S_\omega$ of rapidly decreasing $\omega$-ultradifferentiable functions is nuclear for every weight function $\omega(t)=o(t)$ as $t$ tends to infinity. Moreover, we prove that,
Schindl, Gerhard +8 more
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How far is the Borel map from being surjective in quasianalytic ultradifferentiable classes?, [PDF]
, 2018 peer reviewedThe Borel map $j^{\infty}$ takes germs at 0 of smooth functions to the sequence of iterated partial derivatives at 0. In the literature, it is well known that the restriction of $j^{\infty}$ to the germs of quasianalytic ultradifferentiable ...
Schindl, Gerhard, Esser, Céline
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Nonlinear conditions for ultradifferentiability: a uniform approach [PDF]
, 2022 Recent work showed that a theorem of Joris (that a function $f$ is smooth if two coprime powers of $f$ are smooth) is valid in a wide variety of ultradifferentiable classes $\mathcal C$. The core of the proof was essentially $1$-dimensional.
Nenning, David Nicolas +2 more
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Extension Operators for Some Ultraholomorphic Classes Defined by Sequences of Rapid Growth [PDF]
, 2023 While the asymptotic Borel mapping, sending a function into its series of asymptotic expansion in a sector, is known to be surjective for arbitrary openings in the framework of ultraholomorphic classes associated with sequences of rapid growth, there is ...
Alberto Lastra +5 more
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The Gabor wave front set in spaces of ultradifferentiable functions [PDF]
, 2019 [EN] We consider the spaces of ultradifferentiable functions S as introduced by Bjorck (and its dual S) and we use time-frequency analysis to define a suitable wave front set in this setting and obtain several applications: global regularity properties ...
Jornet Casanova, David +4 more
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The Borel map in the mixed Beurling setting [PDF]
, 2022 The Borel map takes a smooth function to its infinite jet of derivatives (at zero). We study the restriction of this map to ultradifferentiable classes of Beurling type in a very general setting which encompasses the classical Denjoy-Carleman and Braun ...
Nenning, David Nicolas +2 more
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Ultradifferentiable functions on lines in ℝⁿ [PDF]
Proceedings of the American Mathematical Society, 1999 It is well known that a function f ∈
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ITEGAM-JETIAIn this article, we demonstrate the weakly hyperbolic Cauchy problem under Hölder's regularity of a coefficient depending on time in the context of M-ultradifferentiable well-posedness.
Said Bouaziz +2 more
doaj +1 more source
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
wiley +1 more source