- journal article metadata
European Mathematical Society Publishing House
2018-03-11 23:30:00
Journal of the European Mathematical Society
J. Eur. Math. Soc.
JEMS
1435-9855
1435-9863
General
10.4171/JEMS
http://www.ems-ph.org/doi/10.4171/JEMS
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
20
2018
3
Christoffel functions with power type weights
Tivadar
Danka
University of Szeged, Hungary
Vilmos
Totik
University of Szeged, Hungary and University of South Florida, USA
Christoffel functions, asymptotics, power type weights, Jordan curves and arcs, Bessel functions, fast decreasing polynomials, equilibrium measures
Precise asymptotics for Christoffel functions are established for power type weights on unions of Jordan curves and arcs. The asymptotics involve the equilibrium measure of the support of the measure. The result at the endpoints of arc components is obtained from the corresponding asymptotics for internal points with respect to a different power weight. On curve components the asymptotic formula is proved via a sharp form of Hilbert's lemniscate theorem while taking polynomial inverse images. The situation is completely different on the arc components, where the local asymptotics is obtained via a discretization of the equilibrium measure with respect to the zeros of an associated Bessel function. The proofs are potential theoretical, and fast decreasing polynomials play an essential role in them.
Potential theory
Real functions
Approximations and expansions
Fourier analysis
747
796
10.4171/JEMS/776
http://www.ems-ph.org/doi/10.4171/JEMS/776
2
27
2018