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Power bounded composition operators on spaces of analytic functions [PDF]

Collectanea Mathematica, 2010
We study the dynamical behaviour of composition operators defined on spaces of real analytic functions. We characterize when such operators are power bounded, i.e. when the orbits of all the elements are bounded. In this case this condition is equivalent
JOSÉ Bonet, Paweł Domanski, Bonet JOSÉ   +2 more
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Analytical evaluation of Fukui functions and real-space linear response function

The Journal of Chemical Physics, 2012
Many useful concepts developed within density functional theory provide much insight for the understanding and prediction of chemical reactivity, one of the main aims in the field of conceptual density functional theory. While approximate evaluations of such concepts exist, the analytical and efficient evaluation is, however, challenging, because such ...
Yang, W., Cohen, J., De Proft, Frank, Geerlings, Paul   +3 more
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Composition operators on spaces of real analytic functions

Mathematische Nachrichten, 2003
AbstractLet Ω1, Ω2be open subsets of ℝand ℝ, respectively, and let A(Ω1) denote the space of real analytic functions on Ω1. We prove a Glaeser type theorem by characterizing when a composition operatorCφ: A(Ω1) → A(Ω2),Cφ(f) ≔f∘φ, is a topological embedding.
Domański, Paweł, Langenbruch, Michael
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Convolution operator in the space of real analytic functions

Mathematical Notes of the Academy of Sciences of the USSR, 1991
Soit \(\omega\subset\mathbb{R}\) un intervalle (borné ou non-borné). On définit l'opérateur différentiel d'ordre infini \(M_ \varphi: A(\omega)\to A(\omega)\), où \(A(\omega)\) est l'ensemble des fonctions analytiques sur \(\omega\), par \(M_ \varphi u=\sum_{0\leq k\leq\infty} a_ k u^{(k)}\), \(a_ k\in\mathbb{C}\).
Napalkov, V. V., Rudakov, I. A.
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A non-trivial Fr�chet quotient of the space of real analytic functions

Archiv der Mathematik, 2003
In their earlier article [\textit{P. Domański} and \textit{D. Vogt}, Stud. Math. 142, 187--200 (2000; Zbl 0990.46015)], the authors proved the spectacular result that the space \({\mathcal A}(\Omega)\) of all complex-valued real-analytic functions on an open set \(\Omega \subset \mathbb{R}^d\), endowed with its natural locally convex topology, does not
Domański, Paweł, Vogt, Dietmar
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A note on composition operators on spaces of real analytic functions

Annales Polonici Mathematici, 2012
We characterize composition operators on spaces of real analytic functions which are open onto their images. We give an example of a semi-proper map φ such that the associated composition operator is not open onto its image.
Paweł Domański, Michał Goliński, Michael Langenbruch   +2 more
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The coherence of complemented ideals in the space of real analytic functions

Mathematische Annalen, 2009
If \( V \) is a complex analytic subvariety of a complex neighborhood of \( \mathbb R^d \), then its ideal \( J_V(\mathbb R^d) \) is defined as the set of all real analytic functions on \( \mathbb R^d \) such that any extension to a holomorphic function on a neighborhood of \( \mathbb R^d \) vanishes in a neighborhood, relative to \( V \), of \( X = V \
Domański, Paweł, Vogt, Dietmar
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Analytic Representations and Fourier Transforms of Analytic Functionals in $Z'$ Carried by the Real Space

SIAM Journal on Mathematical Analysis, 1978
In the space $Z'$, the Fourier transform of the space $\mathcal{D}'$ of Schwartz-distributions, the notion of carrier is introduced. A characterization is given of all distributions $\mathcal{D}'$, the Fourier transform of which is carried by $\mathbb{R}^n $.
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COMPOSITION OPERATORS WITH CLOSED IMAGE ON SPACES OF REAL ANALYTIC FUNCTIONS

Bulletin of the London Mathematical Society, 2006
We characterize composition operators on spaces of real analytic functions which at the same time have closed image and are open onto their images. Under some mild assumptions, we also characterize composition operators with closed range and composition operators open onto their images.
P. DOMANSKI, M. LANGENBRUCH
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Algebra of multipliers on the space of real analytic functions of one variable

Studia Mathematica, 2012
We consider the topological algebra of (Taylor) multipliers on spaces of real analytic functions of one variable, i.e., maps for which monomials are eigenvectors. We describe multiplicative functionals and algebra homomorphisms on that algebra as well as idempotents in it. We show that it is never a Q-algebra and never locally m-convex.
Paweł Domański, Michael Langenbruch
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