Beurling-Landau densities of weighted Fekete sets and correlation kernel estimates

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Beurling-Landau densities of weighted Fekete sets and correlation kernel estimates. / Ameur, Yacin; Ortega-Cerda, Joaquim.

In: Journal of Functional Analysis, Vol. 263, No. 7, 2012, p. 1825-1861.

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TY - JOUR

T1 - Beurling-Landau densities of weighted Fekete sets and correlation kernel estimates

AU - Ameur, Yacin

AU - Ortega-Cerda, Joaquim

PY - 2012

Y1 - 2012

N2 - Let Q be a suitable real function on C. An n-Fekete set corresponding to Q is a subset {z(n vertical bar) , . . . , z(nn)} of C which maximizes the expression Pi(n)(i infinity. In this note we prove that Fekete sets are, in a sense, maximally spread out with respect to the equilibrium measure. In general, our results apply only to a part of the Fekete set, which is at a certain distance away from the boundary of the droplet. However, for the potential Q = vertical bar z vertical bar(2) we obtain results which hold globally, and we conjecture that such global results are true for a wide range of potentials. (C) 2012 Elsevier Inc. All rights reserved.

AB - Let Q be a suitable real function on C. An n-Fekete set corresponding to Q is a subset {z(n vertical bar) , . . . , z(nn)} of C which maximizes the expression Pi(n)(i infinity. In this note we prove that Fekete sets are, in a sense, maximally spread out with respect to the equilibrium measure. In general, our results apply only to a part of the Fekete set, which is at a certain distance away from the boundary of the droplet. However, for the potential Q = vertical bar z vertical bar(2) we obtain results which hold globally, and we conjecture that such global results are true for a wide range of potentials. (C) 2012 Elsevier Inc. All rights reserved.

KW - Weighted Fekete set

KW - Droplet

KW - Equidistribution

KW - Concentration operator

KW - Correlation kernel

U2 - 10.1016/j.jfa.2012.06.01

DO - 10.1016/j.jfa.2012.06.01

M3 - Article

VL - 263

SP - 1825

EP - 1861

JO - Journal of Functional Analysis

T2 - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 7

ER -