| Weyl and Lidski? Inequalities for General Hyperbolic Polynomials |
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| 作者姓名： | Denis SERRE |
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| 基金项目： | Acknowledgements Although the author began to think about this problem when he prepared his book on matrices （Springer-Verlag, GTM # 216 （2002）） and the book with S. Benzoni-Gavage on multi-dimensional hyperbolic IBVP （Oxford University Press （2007））, it is fair to say that he learnt a lot about hyperbolic polynomials during his stay in Mittag-Leffler Institute in autumn 2005. The author keeps a deep impression of the marvelous library there, and the warm working atmosphere. It is thus a great pleasure to thank S. Benzoni-Gavage for her fruitful collaboration and the Mittag-Leffler Institute for its hospitality. The author has benefited also from the sustained interest of Peter Lax on that work. |
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| 摘 要： | The roots of hyperbolic polynomials satisfy the linear inequalities that were previously established for the eigenvalues of Hermitian matrices, after a conjecture by A. Horn. Among them are the so-called Weyl and Lidskiǐ inequalities. An elementary proof of the latter for hyperbolic polynomials is given. This proof follows an idea from H. Weinberger and is free from representation theory and Schubert calculus arguments, as well as from hyperbolic partial differential equations theory.
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| 关 键 词： | 多项式的根 线性不等式 双曲型 偏微分方程理论 埃尔米特矩阵 初等证明 特征值 温伯格 |
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