On a Sequence of Fast Decreasing Polynomial Operators

Mhaskar, Hrushikesh N.; Prestin, Jürgen

doi:10.1007/978-3-0348-8685-7_12

Hrushikesh N. Mhaskar¹¹ &
Jürgen Prestin¹²

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 131))

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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.

Article Note

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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Authors and Affiliations

Department of Mathematics, California State University, Los Angeles, CA, 90032, USA
Hrushikesh N. Mhaskar
GSF — National Research Institute for Environment and Health, Institute of Biomathematics and Biometrics, D-85764, Neuherberg, Germany
Jürgen Prestin

Authors

Hrushikesh N. Mhaskar
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Jürgen Prestin
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Editors and Affiliations

Department of Computer Sciences, Purdue University, West Lafayette, IN, 47907-1398, USA
Walter Gautschi
Institute for Applied Mathematics, University of Hamburg, Bundesstr. 55, D-20146, Hamburg, Germany
Gerhard Opfer
Computer Science Department, Stanford University, Stanford, CA, 94305, USA
Gene H. Golub

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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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