On certain regularity properties of Haar-null sets

Pandelis Dodos

Displaying similar documents to “On certain regularity properties of Haar-null sets”

Complexity of the class of Peano functions

K. Omiljanowski, S. Solecki, J. Zielinski (2000)

Colloquium Mathematicae

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We evaluate the descriptive set theoretic complexity of the space of continuous surjections from $ℝ^{m}$ to $ℝ^{n}$ .

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K. Adžievski (1986)

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Analytic and $C^{k}$ approximations of norms in separable Banach spaces

Robert Deville, Vladimir Fonf, Petr Hájek (1996)

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On the analyticity of generalized eigenfunctions (case of real variables)

Eberhard Gerlach (1968)

Annales de l'institut Fourier

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On démontre que, dans les espaces fonctionnels propres de Hilbert (avec un noyau reproduisant), formés de fonctions analytiques de $n$ variables dans un domaine $G$ , pour tout opérateur auto-adjoint, les fonctions propres généralisées sont des fonctions réelles-analytiques dans $G$ .

Spaces of D-paraanalytic elements

D. Przeworska-Rolewicz

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Let X be a linear space. Consider a linear equation(*) P(D)x = y, where y ∈ E ⊂ X,with a right invertible operator D ∈ L(X) and, in general, operator coefficients. The main purpose of this paper is to characterize those subspaces E ⊂ X for which all solutions of (*) belong to E (provided that they exist). This leads, even in the classical case of ordinary differential equations with scalar coefficients, to a new class of $C^{\infty}$ -functions, which properly contains the classes of analytic functions...

On the Pythagoras numbers of real analytic set germs

José F. Fernando, Jesús M. Ruiz (2005)

Bulletin de la Société Mathématique de France

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We show that (i) the Pythagoras number of a real analytic set germ is the supremum of the Pythagoras numbers of the curve germs it contains, and (ii) every real analytic curve germ is contained in a real analytic surface germ with the same Pythagoras number (or Pythagoras number $2$ if the curve is Pythagorean). This gives new examples and counterexamples concerning sums of squares and positive semidefinite analytic function germs.

Overstability and resonance

Augustin Fruchard, Reinhard Schäfke (2003)

Annales de l’institut Fourier

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We consider a singularity perturbed nonlinear differential equation $ε u^{'} = f (x) u + + ε P (x, u, ε)$ which we suppose real analytic for $x$ near some interval $[a, b]$ and small $| u |$ , $| ε |$ . We furthermore suppose that 0 is a turning point, namely that $x f (x)$ is positive if $x \neq 0$ . We prove that the existence of nicely behaved (as $ϵ \to 0$ ) local (at $x = 0$ ) or global, real analytic or $C^{\infty}$ solutions is equivalent to the existence of a formal series solution $\sum u_{n} (x) ε^{n}$ with $u_{n}$ analytic at $x = 0$ . The main tool of a proof is a new “principle of analytic continuation” for...

On analyticity in cosmic spaces

Oleg Okunev (1993)

Commentationes Mathematicae Universitatis Carolinae

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We prove that a cosmic space (= a Tychonoff space with a countable network) is analytic if it is an image of a $K$ -analytic space under a measurable mapping. We also obtain characterizations of analyticity and $σ$ -compactness in cosmic spaces in terms of metrizable continuous images. As an application, we show that if $X$ is a separable metrizable space and $Y$ is its dense subspace then the space of restricted continuous functions $C_{p} (X ∣ Y)$ is analytic iff it is a $K_{σ δ}$ -space iff $X$ is $σ$ -compact. ...

Co-analytic, right-invertible operators are supercyclic

Sameer Chavan (2010)

Colloquium Mathematicae

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Let denote a complex, infinite-dimensional, separable Hilbert space, and for any such Hilbert space , let () denote the algebra of bounded linear operators on . We show that for any co-analytic, right-invertible T in (), αT is hypercyclic for every complex α with $| α | > β^{- 1}$ , where $β \equiv i n f_{| | x | | = 1} | | T * x | | > 0$ . In particular, every co-analytic, right-invertible T in () is supercyclic.