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On the number of roots of exp-trig polynomials

Über die Anzahl der Nullstellen von polynomial-trigonometrischen Exponentialsummen

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Abstract

The number of roots, on an interval of lengthT, ofc′ e At b≢0 is at most (n-1)[T ω/π]*, wheren is the dimension ofA, b, c; ω is the largest imaginary part of eigenvalue ofA, and [x]* denotes the smallest integerk≥x.

Zusammenfassung

Eine Funktion der Formc′ e At b≢0 hat höchstens (n-1)[T ω/π]* Nullstellen in einem Intervall der LängeT, wobein die Dimension vonA, b, c ist, ω der größte Imaginärteil der Eigenwerte vonA und [x]* die kleinste ganze Zahlk≥x.

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References

  1. Chukwu, E. N., Hájek, O.: Disconjugacy and optimal control (to appear in Journ. Opt. Th. and Appl.).

  2. Collatz, L., Krabs, W.: Approximationstheorie. Stuttgart: Teubner 1973.

    Google Scholar 

  3. Hájek, O.: Optimal controls with side constraints (in preparation).

  4. Hájek, O.: Terminal manifolds and switching locus. Math. Syst. Theory6, 289–301 (1973).

    Google Scholar 

  5. Kolumbán, I.: Über die nichtlineare trigonometrische Approximation, pp. 69–72, in: Numerische Methoden der Approximationstheorie, Bd. 2 (Collatz, L., Meinardus, G., eds.). Basel: Birkhäuser 1975.

    Google Scholar 

  6. Lee, E. B., Markus, L.: Foundations of Optimal Control Theory. New York: Wiley 1967.

    Google Scholar 

  7. Levinson, N.: Minimax Liapunov and “bang-bang”. J. Diff. Equations2, 218–241 (1966).

    Google Scholar 

  8. Meinardus, G.: Über ein Problem von L. Collatz. Computing8 250–254 (1971).

    Google Scholar 

  9. Pólya, G., Szegö, G.: Problems and Theorems in Analysis, Vol. 1. Berlin-Heidelberg-New York: Springer 1972.

    Google Scholar 

  10. Yeung, D. S.: Synthesis of time-optimal control. Ph. D. Thesis, Case Western Reserve University, Cleveland, Ohio, 1974.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Case Western Reserve University, 44106, Cleveland, OH, USA

    O. Hájek

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  1. O. Hájek
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Additional information

This paper was prepared while the author held a Humboldt Award at TH Darmstadt, Fachbereich Mathematik, Arbeitsgruppe 10.

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Hájek, O. On the number of roots of exp-trig polynomials. Computing 18, 177–183 (1977). https://doi.org/10.1007/BF02243627

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  • DOI: https://doi.org/10.1007/BF02243627

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