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Young, N. J.

An identity which implies Cohn’s theorem on the zeros of a polynomial. (English) Zbl 0415.30004

J. Math. Anal. Appl. 70, 240-248 (1979).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
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Cited in 7 Documents

MSC:

30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
30C10 Polynomials and rational functions of one complex variable
12D10 Polynomials in real and complex fields: location of zeros (algebraic theorems)

Keywords:

location of zeros of polynomials
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References:

[1] Cohn, A., Über die Anzahl der Wurzeln einer algebraischen Gleichung in einem Kreise, Math. Z., 14, 110-148 (1922) · JFM 48.0083.01
[2] Gantmacher, F. R., Applications of the Theory of Matrices (1959), Interscience: Interscience New York/London · Zbl 0085.01001
[3] Hermite, C., Sur le nombre des racines d’une équation algébrique comprises entre des limites données, J. Reine Angew. Math., 52, 39-51 (1856) · ERAM 052.1365cj
[4] Jury, E. I., Inners and Stability of Dynamic Systems (1974), Wiley: Wiley New York · Zbl 0307.93025
[5] Marden, M., The Geometry of the Zeros of a Polynomial in a Complex Variable (1949), Amer. Math. Soc: Amer. Math. Soc New York · Zbl 0038.15303
[6] Parks, P. C., Liapunov and the Schur-Cohn stability criterion, IEEE Trans. Automatic Control, 9, 121 (1964)
[7] Potapov, V. P., The multiplicative structure of \(J\)-contractive matrix functions, Amer. Math. Soc. Transl., 15, 131-243 (1960) · Zbl 0090.05403
[8] Routh, E. J., (Fuller, A. T., Stability of Motion (1975), Taylor & Francis: Taylor & Francis London), (edited and introduced by A. T. Fuller) · JFM 10.0628.03
[9] Young, N. J., Norms of powers of matrices with constrained spectra, Linear Algebra Appl., 23, 227-244 (1979) · Zbl 0401.15014
[10] N. J. YoungInt. J. Control; N. J. YoungInt. J. Control · Zbl 0432.93050
[11] Lancaster, P., Theory of Matrices (1969), Academic Press: Academic Press New York · Zbl 0186.05301
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