Positive trigonometric polynomials
作者： Vladimir Tkachev
DOI:
关键词:
摘要: We study the boundary of nonnegative trigonometric polynomials from algebraic point view. In particularly, we show that it is a subset an irreducible hypersurface and established its explicit form in terms resultants.
arxiv.org
harvard.edu参考文章(9)
Walter Van Assche, Orthogonal polynomials in the complex plane and on the real line Fields Institute Communications. ,vol. 14, pp. 211- 245 ,(1997)
Uspensky, J. V. , b., Theory of Equations. ,(1958)
G. E. Wall, D. E. Littlewood, A university algebra The Mathematical Gazette. ,vol. 36, pp. 63- ,(1952) , 10.2307/3610789
Stephen Hoffman, N. I. Akhiezer, The Classical Moment Problem. American Mathematical Monthly. ,vol. 75, pp. 100- ,(1968) , 10.2307/2315170
David A. Brannan, On univalent polynomials Glasgow Mathematical Journal. ,vol. 11, pp. 102- 107 ,(1970) , 10.1017/S0017089500000926
J. R. Quine, On univalent polynomials Proceedings of the American Mathematical Society. ,vol. 57, pp. 75- 78 ,(1976) , 10.1090/S0002-9939-1976-0402024-3
D. A. Brannan, Coefficient regions for univalent polynomials of small degree Mathematika. ,vol. 14, pp. 165- 169 ,(1967) , 10.1112/S0025579300003764
Alan Gluchoff, Frederick Hartmann, Univalent Polynomials and Non-Negative Trigonometric Sums American Mathematical Monthly. ,vol. 105, pp. 508- 522 ,(1998) , 10.1080/00029890.1998.12004919
Richard Askey, George Gasper, Inequalities for polynomials The Bieberbach Conjecture: Proceedings of the Symposium on the Occasion of the Proof. pp. 7- 32 ,(1986) , 10.1090/SURV/021/02