Fekete interpolation sites for a continuous function space

ID: fekete-interpolation-sites-for-a-continuous-function-space

For a real -dimensional vector space of continuous functions on a compact interval, choose sites maximizing the absolute evaluation determinant in any basis. Linear independence ensures some nonzero evaluation determinant, so a maximizer exists and has distinct sites. Replacing row by evaluation at multiplies the determinant by the cardinal function . Maximality implies , hence the Lebesgue constant of interpolation is at most . This gives a useful interpolation set without asserting that determinant maximization minimizes the Lebesgue constant of interpolation.

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