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Acta Mathematica Hungarica

, Volume 158, Issue 1, pp 216–234 | Cite as

Christoffel functions on planar domains with piecewise smooth boundary

  • A. PrymakEmail author
  • O. Usoltseva
Article
  • 24 Downloads

Abstract

Up to a constant factor, we compute the Christoffel function on planar domains with boundary consisting of finitely many C2 curves such that each corner point of the boundary has interior angle strictly between 0 and \(\pi \). The resulting formula uses the distances from the point of interest to the curves or certain parts of the curves defining the boundary of the domain.

Key words and phrases

Christoffel function algebraic polynomial orthogonal polynomial boundary effect 

Mathematics Subject Classification

42C05 41A17 41A63 26D05 42B99 

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Notes

Acknowledgement

We are grateful to the referee for the careful reading of the manuscript and several valuable suggestions that pointed out some inaccuracies and, more importantly, led to an improvement of the generality of the result.

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ManitobaWinnipegCanada

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