Harmonic Analysis/Dynamical Systems
Methods of harmonic analysis in nonlinear dynamics
Comptes Rendus. Mathématique, Volume 351 (2013) no. 9-10, pp. 367-370.

For a pair of conjugate trigonometric polynomials C(t)=j=1Najcosjt, S(t)=j=1Najsinjt, normalized by the condition j=1Naj=1, the following extremal value is found:

supa1,,aNmint{C(t):S(t)=0}=tan2π2(N+1).
An application of this result in the control theory for nonlinear discrete systems is shown.

Pour un couple de polynômes trigonométriques C(t)=j=1Najcosjt, S(t)=j=1Najsinjt, normalisés par la condition j=1Naj=1, on a la formule extrémale suivante :

supa1,,aNmint{C(t):S(t)=0}=tan2π2(N+1).
On donne une application de ce résultat en théorie du contrôle à des systèmes non linéaires discrets.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2013.05.009
Dmitrishin, Dmitriy 1; Khamitova, Anna 2

1 Odessa National Polytechnic University, 1 Shevchenko Ave., Odessa 65044, Ukraine
2 Georgia Southern University, Statesboro, GA 30460, USA
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Dmitrishin, Dmitriy; Khamitova, Anna. Methods of harmonic analysis in nonlinear dynamics. Comptes Rendus. Mathématique, Volume 351 (2013) no. 9-10, pp. 367-370. doi : 10.1016/j.crma.2013.05.009. http://www.numdam.org/articles/10.1016/j.crma.2013.05.009/

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