Christoffel functions on planar domains with piecewise smooth boundary
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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 phrasesChristoffel function algebraic polynomial orthogonal polynomial boundary effect
Mathematics Subject Classification42C05 41A17 41A63 26D05 42B99
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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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