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On Constrained L2-Approximation of Complex Functions

Published online by Cambridge University Press:  20 November 2018

M. A. Bokhari
M. A. Bokhari*
Affiliation:
Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261 Saudi Arabia, e-mail:[email protected]
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Abstract

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A function f analytic in any disc of radius greater than 1 is approximated in the L2-sense over a class of polynomials which also interpolate f on a subset of the roots of unity. The resulting solution is used to discuss Walsh-type equiconvergence. The main theorem of the paper generalizes certain results of Walsh, Rivlin and Cavaretta et al.

Keywords

30E1041A20Taylor's polynomialLagrange interpolantl2 and L2 minimizationinner product spaceequiconvergence
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 2 , 01 June 1995 , pp. 149 - 155
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Cavaretta, A. S. Jr., Sharma, A. and Varga, R. S., Interpolation in the roots of unity: an extension of a Theorem of J. L. Walsh, Resultate Math. 3(1981), 155–191.Google Scholar
2. Ivanov, K. G. and Sharma, A., Converse results on equiconvergence of interpolating polynomials, Anal. Math. 14(1988), 185–192.Google Scholar
3. Ivanov, K. G., More quantitative results on Walsh equiconvergence. I. Lagrange case, Constr. Approx. 3(1987), 265–280.Google Scholar
4. Rivlin, T. J., On Walsh equiconvergence, J. Approx. Theory 36(1982), 334–345.Google Scholar
5. Saffand, E. B. Varga, R. S., A note on the sharpness of J. L. Walsh s theorem and its extensions for interpolation in the roots of unity, Acta Math. Hungar. 41(1983), 371—377.Google Scholar
6. Sharma, A. and Ziegler, Z., Walsh equiconvergence for best fa-Approximates, Studia Math. LXXVII(1984), 523–528.Google Scholar
7. Szabados, J., Converse results in the theory of overconvergence of complex interpolating polynomials, Analysis 2(1982), 267–280.Google Scholar
8. Totik, V., Quantitative results in the theory of overconvergence of complex interpolating polynomials, J. Approx. Theory 47(1986), 173–183.Google Scholar
9. Walsh, J. L., Interpolation and Approximation by Rational Functions in the Complex Domain, 5th éd., Amer. Math. Soc, Providence, Rhode Island, 1969.Google Scholar