Titlebook: Discrepancy of Signed Measures and Polynomial Approximation; Vladimir V. Andrievskii,Hans-Peter Blatt Book 2002 Springer Science+Business

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Book 2002with respect to the angular measure. In 1929 Bernstein [27] stated the following theorem. Let f be a positive continuous function on [-1, 1]; if almost all zeros of the polynomials of best 2 approximation to f (in a weighted L -norm) are outside of an open ellipse c with foci at -1 and 1, then f has

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Praktische Verfahren und Rezepte,ce .. := {.: |.| = .} is a limit point of zeros of polynomials ..(.), . = 1, 2,... . Szeg? [170] substantially improved this result by showing that there is a subsequence .% MathType!MTEF!2!1!+-% feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharq

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Discrepancy of Signed Measures and Polynomial Approximation

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Discrepancy Theorems via One-Sided Bounds for Potentials,urve or arc .. The basic quantities involved have been the two terms . and . where .. ∈ int . is fixed if . is a curve. In Section 2.3 we have outlined that it is possible to restrict the essential quantities to the .. in the case of a Jordan arc. If . is a curve, we replace .. by the smaller .. whe

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Applications of Discrepancy Theorems,sets . of ?. It is known that the counting measures for Fekete point sets converge to the equilibrium distribution of .. Furthermore, if . is a Jordan curve or arc, then this weak*-convergence can be estimated by discrepancy bounds. For analytic Jordan curves Pommerenke [144, 145] has proved sharp a

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978-1-4419-3146-7Springer Science+Business Media New York 2002