The Experts below are selected from a list of 318 Experts worldwide ranked by ideXlab platform
Stéphanie Nivoche - One of the best experts on this subject based on the ideXlab platform.
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Proof of a conjecture of Zahariuta concerning a problem of Kolmogorov on the ε-entropy
Inventiones mathematicae, 2004Co-Authors: Stéphanie NivocheAbstract:We prove a conjecture of Zahariuta which itself solves a problem of Kolmogorov on the ε-entropy of some classes of analytic functions. For a given holomorphically convex Compact Subset K in a pseudoconvex domain D in C ^ n , Zahariuta’s conjecture consists in approximating the relative extremal function u ^*_ K , D , uniformly on any Compact Subset of D ∖ K , by pluricomplex Green functions on D with logarithmic poles in the Compact Subset K .
Ragnar Sigurdsson - One of the best experts on this subject based on the ideXlab platform.
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SICIAK-ZAHARIUTA EXTREMAL FUNCTIONS, ANALYTIC DISCS AND POLYNOMIAL HULLS
Mathematische Annalen, 2009Co-Authors: Finnur Larusson, Ragnar SigurdssonAbstract:We prove two disc formulas for the Siciak–Zahariuta extremal function of an arbitrary open Subset of complex affine space. We use these formulas to characterize the polynomial hull of an arbitrary Compact Subset of complex affine space in terms of analytic discs. Similar results in previous work of ours required the Subsets to be connected.
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Siciak-Zahariuta extremal functions and polynomial hulls
arXiv: Complex Variables, 2007Co-Authors: Finnur Larusson, Ragnar SigurdssonAbstract:We use our disc formula for the Siciak-Zahariuta extremal function to characterize the polynomial hull of a connected Compact Subset of complex affine space in terms of analytic discs.
Vladimir V. Andrievskii - One of the best experts on this subject based on the ideXlab platform.
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Bernstein Polynomial Inequality on a Compact Subset of the Real Line
arXiv: Complex Variables, 2018Co-Authors: Vladimir V. AndrievskiiAbstract:We prove an analogue of the classical Bernstein polynomial inequality on a Compact Subset $E$ of the real line. The Lipschitz continuity of the Green function for the complement of $E$ with respect to the extended complex plane and the differentiability at a point of $E$ of a special, associated with $E$, conformal mapping of the upper half-plane onto the comb domain play crucial role in our investigation.
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Polynomial approximation on a Compact Subset of the real line
Journal of Approximation Theory, 2018Co-Authors: Vladimir V. AndrievskiiAbstract:Abstract We prove an analogue of the classical Bernstein theorem concerning the rate of polynomial approximation of piecewise analytic functions on a Compact Subset of the real line.
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Polynomial approximation of piecewise analytic functions on a Compact Subset of the real line
Journal of Approximation Theory, 2009Co-Authors: Vladimir V. AndrievskiiAbstract:We discuss Totik's extension of the classical Bernstein theorem on polynomial approximation of piecewise analytic functions on a closed interval. The error of the best uniform approximation of such functions on a Compact Subset of the real line is studied.
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On Sparse Sets with the Green Function of the Highest Smoothness
Computational Methods and Function Theory, 2006Co-Authors: Vladimir V. AndrievskiiAbstract:Let E be a regular Compact Subset of the real line, let be the Green function of the complement of E with respect to the extended complex plane ${\overline {\rm C}}$ with pole at ∞. We construct two examples of sets E of the minimum Hausdorff dimension with satisfying the Hölder condition with p = 1/2 either uniformly or locally.
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Uniformly Perfect Subsets of the Real Line and John Domains
Computational Methods and Function Theory, 2004Co-Authors: Vladimir V. AndrievskiiAbstract:Let E be a regular Compact Subset of the real line. We relate the Green function for the complement of E (with respect to the extended complex plane) to some conformal map f. We establish the relationship between the geometry of E and f(E).
Francisco Naranjo - One of the best experts on this subject based on the ideXlab platform.
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Compactness in quasi-Banach function spaces with applications to $$L^1$$ L 1 of the semivariation of a vector measure
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales. Serie A. Matemáticas, 2020Co-Authors: Ricardo Del Campo, Antonio Fernandez, Fernando Mayoral, Francisco NaranjoAbstract:We characterize the relatively Compact Subsets of the order continuous part $$E_a$$ E a of a quasi-Banach function space E showing that the strong connection between Compactness, uniform absolute continuity, uniform integrability, almost order boundedness and L-weak Compactness that appears in the classical setting of Lebesgue spaces remains almost invariant in this new context under mild assumptions. We also present a de la Vallée–Poussin type theorem in this context that allows us to locate each Compact Subset of $$E_a$$ E a as a Compact Subset of a smaller quasi-Banach Orlicz space $$E^\varPhi .$$ E Φ . Our results generalize the previous known results for the Banach function spaces $$L^1(m)$$ L 1 ( m ) and $$L^1_w(m)$$ L w 1 ( m ) associated to a vector measure m and moreover they can also be applied to the quasi-Banach function space $$L^1\left( \Vert m \Vert \right) $$ L 1 ‖ m ‖ associated to the semivariation of m .
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orlicz spaces associated to a quasi banach function space applications to vector measures and interpolation
arXiv: Functional Analysis, 2019Co-Authors: Ricardo Del Campo, Antonio Fernandez, Fernando Mayoral, Francisco NaranjoAbstract:We characterize the relatively Compact Subsets of $L^1\left(\| m \| \right),$ the quasi-Banach function space associated to the semivariation of a given vector measure $m$ showing that the strong connection between Compactness, uniform absolute continuity, uniform integrability, almost order boundedness and L-weak Compactness that appears in the classic setting of Lebesgue spaces remains almost invariant in this new context of the Choquet integration. Also we present a de la Vallee-Poussin type theorem in the context of these spaces $L^1\left(\|m\|\right)$ that allows us to locate each Compact Subset of $L^1\left(\|m\|\right)$ as a Compact Subset of a smaller quasi-Banach Orlicz space $L^\Phi\left(\|m\|\right)$ associated to the semivariation of the measure $m.$
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Rybakov's theorem for vector measures in Fréchet spaces
Indagationes Mathematicae, 1997Co-Authors: Antonio Fernandez, Francisco NaranjoAbstract:AbstractFor a real Fréchet space X with dual X′ the following conditions are equivalent: 1.(a) X admits a continuous norm.2.(b) Every convex and weakly Compact Subset of X is the closed convex hull of its exposed points.3.(c) For every X-valued, countably additive measure ν there exists x′ in X′ such that ν is ¦x′ v¦-continuous
Tijani Pakhrou - One of the best experts on this subject based on the ideXlab platform.
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Best -Simultaneous Approximation in
Journal of Function Spaces, 2017Co-Authors: Tijani PakhrouAbstract:Let be a Banach space. Let and denote by the Banach space of all -valued Bochner -integrable functions on a certain positive complete -finite measure space , endowed with the usual -norm. In this paper, the theory of lifting is used to prove that, for any weakly Compact Subset of , the set is -simultaneously proximinal in for any arbitrary monotonous norm in .
