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On Hadamard powers of polynomials

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Abstract

We introduce the concept of the Hadamard power of a polynomial formed by real powers of its coefficients. We show that the Hadamard power of a Hurwitz polynomial remains Hurwitz.

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References

  1. Gantmacher, F. R., and Krein, M. G.,Oszillationsmatrizen, Oszillationskerne und kleine Schwingungen mechanischer Systeme, Akademie-Verlag, Berlin, 1960.

    Google Scholar 

  2. Garloff, J., and Shrinivasan, B., The Hadamard factorization of Hurwitz and Schur stable polynomials, in Jeltsch, R., and Mansour, M. (eds.),Stability Theory, International Series of Numerical Mathematics, vol. 121, Birkhäuser Verlag, Boston, 1996, pp. 19–21.

    Google Scholar 

  3. Garloff, J., and Wagner, D. G., Hadamard products of stable polynomials are stable.,J. Math. Analy. Appl., vol. 202, no. 3 (1996), pp. 797–809.

    Article  MATH  MathSciNet  Google Scholar 

  4. Householder, A. S.,The Numerical Treatment of a Single Nonlinear Equation, McGraw-Hill, New York, 1970.

    MATH  Google Scholar 

  5. Kemperman, J. H. B., A Hurwitz matrix is totally positive.SIAM J. Math. Anal., vol. 13, no. 2 (1982), pp. 331–341.

    Article  MATH  MathSciNet  Google Scholar 

  6. Pólya, G., and Szegö, G.,Aufgaben und Lehrsätze aus der Analysis, Springer-Verlag, Berlin, 1925.

    MATH  Google Scholar 

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Correspondence to Jiří Gregor.

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Gregor, J., Tiŝer, J. On Hadamard powers of polynomials. Math. Control Signal Systems 11, 372–378 (1998). https://doi.org/10.1007/BF02750398

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  • DOI: https://doi.org/10.1007/BF02750398

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