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Plank problems, polarization and Chebyshev constants
In this work we discuss "plank problems" for complex Banach spaces and in particular for the classical spaces. In the case we obtain optimal results and for finite dimensional complex Banach spaces,Expand
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On Bernstein and Markov-Type Inequalities for Multivariate Polynomials on Convex Bodies
Let pn be a polynomial of m variables and total degree n such that ?pn?C(K)=1, where K?Rm is a convex body. In this paper we discuss some local and uniform estimates for the magnitude of grad pnExpand
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Linear polarization constants of Hilbert spaces
Abstract This paper has been motivated by previous work on estimating lower bounds for the norms of homogeneous polynomials which are products of linear forms. The purpose of this work is toExpand
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Potential Theoretic Approach to Rendezvous Numbers
Abstract.We analyze relations between various forms of energies (reciprocal capacities), the transfinite diameter, various Chebyshev constants and the so-called rendezvous or average number. TheExpand
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Geometry of homogeneous polynomials on non symmetric convex bodies
If $\Delta$ stands for the region enclosed by the triangle in ${\mathsf R}^2$ of vertices $(0,0)$, $(0,1)$ and $(1,0)$ (or simplex for short), we consider the space ${\mathcal P}(^2\Delta)$ of theExpand
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On the Extremal Rays of the Cone of Positive, Positive Definite Functions
The aim of this paper is to investigate the cone of non-negative, radial, positive-definite functions in the set of continuous functions on ℝd. Elements of this cone admit a Choquet integralExpand
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Turán’s extremal problem on locally compact abelian groups
AbstractLet G be a locally compact abelian group (LCA group) and Ω be an open, 0-symmetric set. Let F:= F(Ω) be the set of all continuous functions f: G → ℝ which are supported in Ω and are positiveExpand
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Rearrangements of fourier series
On considere des series de Fourier trigonometriques classiques de fonctions f dans C(T), ou T est le tore R/2πZ. On demontre un theoreme de convergence uniforme de sommes partielles vers f, base surExpand
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On a problem of Turan about positive definite functions
AbstractWe study the following question posed by Tur´an. Suppose Ω is a convex body in Euclideanspace R d which is symmetric with respect to the origin. Of all positive definite functionssupported inExpand
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How magical rendezvous numbers are explained by potential theory
We analyze relations between various forms of energies (reciprocal capacities), the transfinite diameter, various Chebyshev constants and the so called rendezvous or average number. The latter isExpand
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