Abstract
Let f be a piecewise analytic function on the unit interval (respectively, the unit circle of the complex plane). Starting from the Chebyshev (respectively, Fourier) coefficients of f, we construct a sequence of fast decreasing polynomials (respectively, trigonometric polynomials) which “detect” the points where f fails to be analytic, provided f is not infinitely differentiable at these points.
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1This research was supported, in part, by the Alexander von Humboldt foundation and the U.S. Air Force Office of Scientific Research, Grant number F49620-97-1-0211.
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Mhaskar, H.N., Prestin, J. (1999). On a Sequence of Fast Decreasing Polynomial Operators. In: Gautschi, W., Opfer, G., Golub, G.H. (eds) Applications and Computation of Orthogonal Polynomials. International Series of Numerical Mathematics, vol 131. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8685-7_12
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DOI: https://doi.org/10.1007/978-3-0348-8685-7_12
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9728-0
Online ISBN: 978-3-0348-8685-7
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