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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
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[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] J. H. Curtiss, ”Polynomial interpolation in points equidistributed on the unit cirle”, Pacific J. Math. 12 (1962), 863–877. · Zbl 0115.28503 · doi:10.2140/pjm.1962.12.863
[3] D. Gaier, ”Über Interpolation in regelmässig verteilten Punkten mit Nebenbedingungen”, Math. Z. 61 (1954), 119–123. · Zbl 0057.05801 · doi:10.1007/BF01181337
[4] W. Gautschi, ”Attentuation factors in practical Fourier analysis”, Numer. Math. 5 (1972), 373–400. · Zbl 0231.65101
[5] T. Kakahashi, ”On interpolations of analytic functions”, Proc. Japan Akad. 32 (1956), 707–718. · Zbl 0073.06103 · doi:10.3792/pja/1195525208
[6] O. Kiš, ”On trigonometric (0,2)-interpolation” (Russian), Acta Math. Acad. Sci. Hungar. 11 (1960), 255–276. · Zbl 0103.28703 · doi:10.1007/BF02020944
[7] H. D. Kloosterman, ”Derivatives and finite differences”, Duke Math. J. 17 (1950), 169–186. · Zbl 0039.05605 · doi:10.1215/S0012-7094-50-01718-2
[8] G. G. Lorentz and S. D. Riemenschneider, Birkhoff Interpolation, to appear.
[9] M. Marden, Geometry of Polynomials, Mathematical Surveys, No. 3, American Mathematical Society, Providence, Rhode Island, 1966. · Zbl 0162.37101
[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. · Zbl 0443.65108
[11] T. S. Motzkin and A. Sharma, ”Next-to-interpolatory polynomials with multiplicities”, Canad. J. Math. 19 (1967), 16–23. · Zbl 0171.03801 · doi:10.4153/CJM-1967-002-6
[12] Y. Okada, ”On interpolation by polynomials”, Tôhoku Math. J. 48 (1941), 68–70. · JFM 67.0263.01
[13] T. J. Rivlin, ”Some explicit polynomial approximations in the complex plane”, Bull. Amer. Soc. 73 (1967), 467–469. · Zbl 0185.13503 · doi:10.1090/S0002-9904-1967-11785-3
[14] T. J. Rivlin and H. S. Shapiro, ”A unified approach to certain problems of approximation and minimization”, J. Soc. Indust. Applied Math. 9 (1961), 670–699. · Zbl 0111.06103 · doi:10.1137/0109056
[15] A. Sharma, ”Some remarks on lacunary interpolation in the roots of unity”, Israel J. Math. 2 (1964), 41–49. · Zbl 0171.03803 · doi:10.1007/BF02759733
[16] A. Sharma, ”Interpolatory polynomials in z and z in the roots of unity”, Canad. J. Math. 19 (1967), 16–23. · Zbl 0171.03801 · doi:10.4153/CJM-1967-002-6
[17] A. Sharma, ”Lacunary interpolation in the roots of unity”. Z. Angew. Math. Mech. 46 (1966), 127–133. · Zbl 0146.14103 · doi:10.1002/zamm.19660460207
[18] A. Sharma, ”Some poised and nonpoised problems on interpolation”, SIAM Rev. 14 (1972), 129–151. · Zbl 0314.65001 · doi:10.1137/1014004
[19] P. L. J. van Rooij, F. Schurer, and C. R. van Walt van Praag, ”A bibliography on Hermite-Birkhoff interpolation”, Dept. of Mathematics, Eindhoven University of Technology, Dec, 1975, Eindhoven The Netherlands.
[20] J. L. Walsh, Interpolation and Approximation by Rational Functions in the Complex Domain, American Mathematical Society Colloquium Publications Volume XX, Providence, Rhode Island, fifth edition, 1969.
[21] J. L. Walsh and A. Sharma, ldLeast squares approximations and interpolation in the roots of unity”, Pacific J. Math. 14 (1964), 727–730. · Zbl 0192.16802 · doi:10.2140/pjm.1964.14.727
[22] B. M. Baishanski, ”Equiconvergence of interpolating processes”, Rocky Mountain J. Math. (to appear). · Zbl 0469.30026
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