Results 21 to 30 of about 146 (115)
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.
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On the conjugate weight function and ultradifferentiable classes of entire functions. [PDF]
Adv Oper TheoryWe 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 regularity requirements. Therefore,
Schindl G.
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On the Inclusion Relations of Global Ultradifferentiable Classes Defined by Weight Matrices. [PDF]
Mediterr J MathWe study and characterize the inclusion relations of global classes in the general weight matrix framework in terms of growth relations for the defining weight matrices.
Boiti C, Jornet D, Oliaro A, Schindl G.
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Global hypoelliptic vector fields in ultradifferentiable classes and normal forms [PDF]
, 2020 In this paper we prove that a global $omega$-hypoelliptic vector field on the torus $T^n$ can be transformed by a $mathcall{E}_omega}-diffeomorphism of $T^n$ into a vector field with constant coefficients which satisfy a Diophantine condition in terms of
Angela A. Albanese
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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.
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On the equivalence between moderate growth-type conditions in the weight matrix setting [PDF]
, 2022 We study the generalizations of the known equivalent reformulations of condition moderate growth from the single weight sequence to the weight matrix setting. This condition, also known in the literature under the name stability under ultradifferentiable
Schindl, Gerhard
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Extension maps in ultradifferentiable and ultraholomorphic function spaces [PDF]
, 2000 The problem of the existence of extension maps from 0 to ℝ in the setting of the classical ultradifferentiable function spaces has been solved by Petzsche [9] by proving a generalization of the Borel and Mityagin theorems for $C^{∞}$-spaces.
Schmets, Jean, Valdivia, Manuel
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Real Paley-Wiener theorems in spaces of ultradifferentiable functions [PDF]
, 2020 [EN] We develop real Paley-Wiener theorems for classes S-omega of ultradifferentiable functions and related L-p-spaces in the spirit of Bang and Andersen for the Schwartz class. We introduce results of this type for the so-called Gabor transform and give
Jornet Casanova, David +5 more
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On subadditivity-like conditions for associated weight functions [PDF]
, 2021 The aim of this article is to provide characterizations for subadditivity-like growth conditions for the so-called associated weight functions in terms of the defning weight sequence.
Schindl, Gerhard
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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
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