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.
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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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The first author was supported by NSERC of Canada Discovery Grant RGPIN 04863-15.
The second author was supported by the University of Manitoba Graduate Fellowship and by the Department of Mathematics of the University of Manitoba.
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Prymak, A., Usoltseva, O. Christoffel functions on planar domains with piecewise smooth boundary. Acta Math. Hungar. 158, 216–234 (2019). https://doi.org/10.1007/s10474-019-00945-2
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DOI: https://doi.org/10.1007/s10474-019-00945-2