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Inverse spectral problem for normal matrices and a generalization of the Gauss-Lucas theorem | S. M. Malamud
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12 Apr 2003 | Subject: | Complex Variables; Spectral Theory MSC-class: 15A29; 30C10; 30C15 | math.CV math.SP | Abstract: | We estabish an analog of the Cauchy-Poincare separation theorem for normal matrices in terms of majorization. Moreover, we present a solution to the inverse spectral problem (Borg-type result) for a normal matrix. Using this result we essentially generalize and complement the known Gauss--Lucas theorem on the geometry of the roots of a complex polynomial and of its derivative. In turn the last result is applied to prove the old conjectures of de Bruijn-Springer and Schoenberg about these roots. | Source: | arXiv, math.CV/0304158 | Services: | Forum | Review | PDF | Favorites |
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