Univalent Polynomials and Non-Negative Trigonometric Sums
作者： Alan Gluchoff , Frederick Hartmann
DOI: 10.1080/00029890.1998.12004919
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摘要: where ak, Ak, I-Lk E R. How can ak be chosen so that Pn(z) is univalent on {z: IzI 0 for [0, ,T] or [iT, 17]? Could one easily decide if a given univalent, Tn(6) non-negative? Of all these questions, the second probably easiest to answer. Various positive kernels, example Fejer kernel and Poisson kernel,
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sci-hub.se 参考文章(31)
Eugen Egerv�ry, Abbildungseigenschaften der arithmetischen Mittel der geometrischen Reihe Mathematische Zeitschrift. ,vol. 42, pp. 221- 230 ,(1937) , 10.1007/BF01160074
Jean Dieudonné, Recherches sur quelques problèmes relatifs aux polynômes et aux fonctions bornées d'une variable complexe Annales Scientifiques De L Ecole Normale Superieure. ,vol. 48, pp. 247- 358 ,(1931) , 10.24033/ASENS.812
Richard Askey, Orthogonal Polynomials and Special Functions ,(1975)
L. Fej�r, G. Szeg�, Special conformal mappings Duke Mathematical Journal. ,vol. 18, pp. 535- 548 ,(1951) , 10.1215/S0012-7094-51-01844-3
Jerrold E. Marsden, Michael J. Hoffman, Basic Complex Analysis ,(1973)
G. Szeg�, coefficients Duke Mathematical Journal. ,vol. 8, pp. 559- 564 ,(1941) , 10.1215/S0012-7094-41-00847-5
Leopold Fejér, Über trigonometrische Polynome. Crelle's Journal. ,vol. 146, pp. 53- 82 ,(1916)
M. S. Robertson, Power series with multiply monotonic coefficients. The Michigan Mathematical Journal. ,vol. 16, pp. 27- 31 ,(1969) , 10.1307/MMJ/1029000162
David A. Brannan, On univalent polynomials Glasgow Mathematical Journal. ,vol. 11, pp. 102- 107 ,(1970) , 10.1017/S0017089500000926
G. Pólya, I. J. Schoenberg, Remarks on de la Vallée Poussin means and convex conformal maps of the circle. Pacific Journal of Mathematics. ,vol. 8, pp. 295- 334 ,(1957) , 10.2140/PJM.1958.8.295