Abstract
In this paper some results obtained in last years on complex interpolatory approximation are introduced.
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References
Al’per, S. Ya. and Kalinogorskaja, G.I. (1969) The Convergence of Lagrange interpolation polynomials in the Complex domain, Izv. Vyss. Ucebn. Zaved Math. 11, 13–23.
Chui, C.K. and Shen, X.C. (1989), The degree of approximation by Hermite-Fejer interpolating polynomials in a Jordan domain, Trans. Amer. Math. Coc. (to be submitted)
Curtiss, J.H. (1965) Convergence of complex Lagrange interpolation polynomials on the locus of the interpolation points, Duke Math. J. 32, 187–204.
Gaier, D. (1954) Uber Interpolation in regelmassig verteilten Punkten mit Nebenbedingunger, Math. Zeitschr. 61, 119–133.
Saff, E.B. and Walsh, J.L. (1973) On the convergence of rational function which interpolate in the roots of unity, Pacific J. Math. 45, 639–654.
Sewell, W.E. (1966) Integrated Lipschitz conditions and approximation in the mean by interpolating polynomials, SIAM Num. Anal. 3, 329–343.
Sharma, A. and Szabados, J. (1988) Convergence rates for some lacunary interpolators on the roots of unity, Approx. Theory and its Appl. 4, 41–48.
Sharma, A. and Vertesi, P. (1983) Mean convergence and interpolation in roots of unity, SIAM Math. Anal. 14, 800–806.
Shen, X.C. (1988) On the convergence in the mean of interpolating rational functions, Acta Math. Sinica (to be submitted).
Shen, X.C. (1988) On the convergence of interpolating rational functions in the unite disk, Acta Math. Sinica (to be submitted).
Shen, X.C. (1988) The convergence problem of (0,1,...,q) Hermite-Fejer interpolating polynomials on the roots of unity, Chinese Annals of Math. (to be submitted).
Shen, X.C. (1988) The convergnece problem of (0,1,...,q) Hermite-Fejer interpolating polynomials on the roots of unity II, Chinese Annals of Math. (to be submitted).
Shen, X.C. (1989) On the Approximation in the mean by Birkhoff interpolation on the roots of unity, Approx. Theory I II. Edit. by C.K. Chui et. (to be submitted).
Shen, X.C. and Zhong, L.F. (1988), Approximation by interpolating polynomials in EP(D) spaces, Kexue Tongbao 11, 876.
Shen, X.C. and Zhong, L.F. (1988) Approximation in the mean by Lagrange interpolating polynomial in the complex plane, Kexue Tongbao 33, 810–814.
Szabados, J. and Varma, A.K. (1986) On an open problem of P. Turan concerning Birkhoof interpolation based on the roots of unity, J. Approx. Theory 47, 255–264.
Turan, P. (1980) On some open problem of approximation theory, J. Approx, Theory 29, 23–85.
Varma, A.K. (1988) Complex interpolating polynomials, Proceedings Amer. Math. Soc. 103, 125–130.
Vertesi, P. (1980) Linear operators on the roots of unity, Studia Sci. Math. Hungar. 15, 241–245.
Walsh, J.L. and Sharma, A. (1964) Least squares and interpolation in roots of unity, Pacific J. Math. 14, 727–750.
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© 1989 Birkhäuser Verlag Basel
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Shen, XC. (1989). Some Recent Results on Complex Interpolatory Approximation. In: Multivariate Approximation Theory IV. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 90. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7298-0_34
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DOI: https://doi.org/10.1007/978-3-0348-7298-0_34
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