Ingham type theorems and applications to control theory
Bollettino della Unione matematica italiana, Série 8, 2B (1999) no. 1, pp. 33-63.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

Ingham [6] ha migliorato un risultato precedente di Wiener [23] sulle serie di Fourier non armoniche. Modificando la sua funzione di peso noi otteniamo risultati ottimali, migliorando precedenti teoremi di Kahane [9], Castro e Zuazua [3], Jaffard, Tucsnak e Zuazua [7] e di Ullrich [21]. Applichiamo poi questi risultati a problemi di osservabilità simultanea.
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Baiocchi, Claudio; Komornik, Vilmos; Loreti, Paola. Ingham type theorems and applications to control theory. Bollettino della Unione matematica italiana, Série 8, 2B (1999) no. 1, pp. 33-63. http://geodesic.mathdoc.fr/item/BUMI_1999_8_2B_1_a1/

[1] J. N. J. W. L. CARLESON - P. MALLIAVIN (editors), The Collected Works of Arne Beurling, Volume 2, Birkhäuser (1989).

[2] J. W. S. Cassels , An Introduction to Diophantine Approximation, Cambridge Tracts in Mathematics - Mathematical Physics, No. 45. Cambridge University Press, New York (1957). | MR | Zbl

[3] Castro - E. Zuazua , Une remarque sur les séries de Fourier non-harmoniques et son application à la contrôlabilité des cordes avec densité singulière, C. R. Acad. Sci. Paris Sér. I, 322 (1996), 365-370. | MR | Zbl

[4] K. D. Graham - D. L. Russell , Boundary value control of the wave equation in a spherical region, SIAM J. Control, 13 (1975), 174-196. | MR | Zbl

[5] A. Haraux , Séries lacunaires et contrôle semi-interne des vibrations d'une plaque rectangulaire, J. Math. Pures Appl., 68 (1989), 457-465. | MR | Zbl

[6] A. E. Ingham , Some trigonometrical inequalities with applications in the theory of series, Math. Z., 41 (1936), 367-379. | MR | Zbl

[7] S. Jaffard - M. Tucsnak - E. Zuazua , On a theorem of Ingham, J. Fourier Analysis, to appear. | MR | Zbl

[8] S. Jaffard - M. Tucsnak - E. Zuazua , Singular internal stabilization of the wave equation, J. Differential Equations, to appear. | MR | Zbl

[9] J.-P. Kahane , Pseudo-périodicité et séries de Fourier lacunaires, Ann. Sci. de l'E.N.S., 79 (1962), 93-150. | fulltext mini-dml | MR | Zbl

[10] V. Komornik , Exact Controllability and Stabilization. The Multiplier Method, Collection RMA, Vol. 36, Masson-John Wiley, Paris-Chicester (1994). | MR | Zbl

[11] V. Komornik - P. Loreti , Observabilité frontière de systèmes couplés par analyse non harmonique vectorielle, C. R. Acad. Sci. Paris Sér. I Math., 324 (1997), 895-900. | MR | Zbl

[12] V. Komornik - P. Loreti , Ingham type theorems for vector-valued functions and observability of coupled linear systems, SIAM J. Control Optim., to appear. | MR | Zbl

[13] V. Komornik - P. Loreti , Observability of compactly perturbed systems, submitted. | Zbl

[14] J.-L. Lions , Contrôle des systèmes distribués singuliers, Gauthiers-Villars, Paris (1983). | MR | Zbl

[15] P. Loreti - V. Valente , Partial exact controllability for spherical membranes, SIAM J. Control Optim., 35 (1997), 641-653. | MR | Zbl

[16] Marczinkiewicz - A. Zygmund , Proof of a gap theorem, Duke Math. J., 4 (1938), 469-472. | fulltext mini-dml | MR

[17] N. K. Nikolskii , A Treatise on the Shift Operator, Springer, Berlin (1986). | MR | Zbl

[18] R. E. A. C. Paley - N. Wiener , Fourier Transforms in the Complex Domain, Amer. Math. Soc. Colloq. Publ., Vol. 19, Amer. Math. Soc., New York (1934). | MR | Zbl

[19] K. Seip , On the connection between exponential bases and certain related sequences in $\ell_{2}(-\pi, \pi)$, J. Funct. Anal., 130 (1995), 131-160. | MR | Zbl

[20] P. Turán , On an inequality, Ann. Univ. Sci. Budapest. Eötvös Sect. Math., 1 (1959), 3-6. | MR | Zbl

[21] D. Ullrich , Divided differences and systems of nonharmonic Fourier series, Proc. Amer. Math. Soc., 80 (1980), 47-57. | MR | Zbl

[22] G. N. Watson , A Treatise on the Theory of Bessel Functions, Cambridge University Press (1962). | MR | Zbl

[23] N. Wiener , A class of gap theorems, Ann. Scuola Norm. Sup. Pisa (2), 3 (1934), 367-372. | fulltext mini-dml | MR

[24] R. M. Young , An Introduction to Nonharmonic Fourier Series, Academic Press (1980). | MR | Zbl