×

Interpolation in the roots of unity: An extension of a theorem of J. L. Walsh. (English) Zbl 0447.30020


MSC:

30E05 Moment problems and interpolation problems in the complex plane
30E10 Approximation in the complex plane

Citations:

Zbl 0106.281
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] A. S. Cavaretta, Jr., A. Sharma, and R. S. Varga, “Hermite-Birkhoff interpolation in the n-th roots of unity”, Trans Amer. Math. Soc. (to appear). · Zbl 0431.41001
[2] Curtiss, J. H., Polynomial interpolation in points equidistributed on the unit cirle, Pacific J. Math., 12, 863-877 (1962) · Zbl 0115.28503
[3] Gaier, D., Über Interpolation in regelmässig verteilten Punkten mit Nebenbedingungen, Math. Z., 61, 119-123 (1954) · Zbl 0057.05801
[4] Gautschi, W., Attentuation factors in practical Fourier analysis, Numer. Math., 5, 373-400 (1972) · Zbl 0231.65101
[5] Kakahashi, T., On interpolations of analytic functions, Proc. Japan Akad., 32, 707-718 (1956) · Zbl 0073.06103
[6] Kiš, O., On trigonometric (0,2)-interpolation” (Russian), Acta Math. Acad. Sci. Hungar., 11, 255-276 (1960) · Zbl 0103.28703
[7] Kloosterman, H. D., Derivatives and finite differences, Duke Math. J., 17, 169-186 (1950) · Zbl 0039.05605
[8] G. G. Lorentz and S. D. Riemenschneider, Birkhoff Interpolation, to appear. · Zbl 1159.41001
[9] Marden, M., Geometry of Polynomials, Mathematical Surveys, No. 3 (1966), Rhode Island: American Mathematical Society, Providence, Rhode Island · Zbl 0173.02703
[10] Günter Meinardus, “Schnelle Fourier-Transformation”, Numerische Methoden der Approximationstheorie (L. Collatz, G. Meinardus, H. Werner, eds.), Band 4, pp. 192-203, ISNM vol. 42, Birkhäuser Verlag, Basel and Stutgart, 1978.
[11] Motzkin, T. S.; Sharma, A., Next-to-interpolatory polynomials with multiplicities, Canad. J. Math., 19, 16-23 (1967) · Zbl 0171.03801
[12] Okada, Y., On interpolation by polynomials, Tôhoku Math. J., 48, 68-70 (1941) · JFM 67.0263.01
[13] Rivlin, T. J., Some explicit polynomial approximations in the complex plane, Bull. Amer. Soc., 73, 467-469 (1967) · Zbl 0185.13503
[14] Rivlin, T. J.; Shapiro, H. S., A unified approach to certain problems of approximation and minimization, J. Soc. Indust. Applied Math., 9, 670-699 (1961) · Zbl 0111.06103
[15] Sharma, A., Some remarks on lacunary interpolation in the roots of unity, Israel J. Math., 2, 41-49 (1964) · Zbl 0171.03803
[16] Sharma, A., Interpolatory polynomials in z and z^−1 in the roots of unity, Canad. J. Math., 19, 16-23 (1967) · Zbl 0171.03801
[17] Sharma, A., Lacunary interpolation in the roots of unity, Z. Angew. Math. Mech., 46, 127-133 (1966) · Zbl 0146.14103
[18] Sharma, A., Some poised and nonpoised problems on interpolation, SIAM Rev., 14, 129-151 (1972) · Zbl 0314.65001
[19] van Rooij, P. L J.; Schurer, F.; van Walt van Praag, C. R., “A bibliography on Hermite-Birkhoff interpolation”, Dept. of Mathematics, Eindhoven University of Technology, Dec (1975), The Netherlands: Eindhoven, The Netherlands
[20] Walsh, J. L., Interpolation and Approximation by Rational Functions in the Complex Domain, American Mathematical Society Colloquium Publications Volume XX (1969), Rhode Island: Providence, Rhode Island
[21] Walsh, J. L.; Sharma, A., ldLeast squares approximations and interpolation in the roots of unity, Pacific J. Math., 14, 727-730 (1964) · Zbl 0192.16802
[22] B. M. Baishanski, “Equiconvergence of interpolating processes”, Rocky Mountain J. Math. (to appear). · Zbl 0469.30026
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.