Ingham type theorems and applications to control theory

 Access to full text

 Full (PDF)

 Full (DjVu)

1. J. N. J. W. L. CARLESON - P. MALLIAVIN (editors), The Collected Works of Arne Beurling, Volume 2, Birkhäuser (1989). 
2. CASSELS, J. W. S., An Introduction to Diophantine Approximation, Cambridge Tracts in Mathematics - Mathematical Physics, No. 45. Cambridge University Press, New York (1957). Zbl0077.04801MR87708
3. CASTRO, - ZUAZUA, E., 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. Zbl0865.35075MR1408769
4. GRAHAM, K. D.- RUSSELL, D. L., Boundary value control of the wave equation in a spherical region, SIAM J. Control, 13 (1975), 174-196. Zbl0315.93004MR355756
5. HARAUX, A., Séries lacunaires et contrôle semi-interne des vibrations d'une plaque rectangulaire, J. Math. Pures Appl., 68 (1989), 457-465. Zbl0685.93039MR1046761
6. INGHAM, A. E., Some trigonometrical inequalities with applications in the theory of series, Math. Z., 41 (1936), 367-379. Zbl0014.21503MR1545625
7. JAFFARD, S.- TUCSNAK, M.- ZUAZUA, E., On a theorem of Ingham, J. Fourier Analysis, to appear. Zbl0939.42004MR1491935
8. JAFFARD, S.- TUCSNAK, M.- ZUAZUA, E., Singular internal stabilization of the wave equation, J. Differential Equations, to appear. Zbl0920.35029MR1620290
9. KAHANE, J.-P., Pseudo-périodicité et séries de Fourier lacunaires, Ann. Sci. de l'E.N.S., 79 (1962), 93-150. Zbl0105.28601MR154060
10. KOMORNIK, V., Exact Controllability and Stabilization. The Multiplier Method, Collection RMA, Vol. 36, Masson-John Wiley, Paris-Chicester (1994). Zbl0937.93003MR1359765
11. KOMORNIK, V.- LORETI, P., Observabilité frontière de systèmes couplés par analyse non harmonique vectorielle, C. R. Acad. Sci. Paris Sér. I Math., 324 (1997), 895-900. Zbl0880.93006MR1450445
12. KOMORNIK, V.- LORETI, P., Ingham type theorems for vector-valued functions and observability of coupled linear systems, SIAM J. Control Optim., to appear. Zbl0963.93013MR1655862
13. KOMORNIK, V.- LORETI, P., Observability of compactly perturbed systems, submitted. Zbl0952.34047
14. LIONS, J.-L., Contrôle des systèmes distribués singuliers, Gauthiers-Villars, Paris (1983). Zbl0514.93001MR712486
15. LORETI, P.- VALENTE, V., Partial exact controllability for spherical membranes, SIAM J. Control Optim., 35 (1997), 641-653. Zbl0879.93002MR1436643
16. MARCZINKIEWICZ, - ZYGMUND, A., Proof of a gap theorem, Duke Math. J., 4 (1938), 469-472. MR1546068
17. NIKOLSKII, N. K., A Treatise on the Shift Operator, Springer, Berlin (1986). Zbl0587.47036MR827223
18. PALEY, R. E. A. C.- WIENER, N., Fourier Transforms in the Complex Domain, Amer. Math. Soc. Colloq. Publ., Vol. 19, Amer. Math. Soc., New York (1934). Zbl0011.01601MR1451142
19. SEIP, K., On the connection between exponential bases and certain related sequences in ${\mathrm{\ell }}_2\left(-\pi ,\pi \right)$, J. Funct. Anal., 130 (1995), 131-160. Zbl0872.46006MR1331980
20. TURÁN, P., On an inequality, Ann. Univ. Sci. Budapest. Eötvös Sect. Math., 1 (1959), 3-6. Zbl0092.29001MR101445
21. ULLRICH, D., Divided differences and systems of nonharmonic Fourier series, Proc. Amer. Math. Soc., 80 (1980), 47-57. Zbl0448.42009MR574507
22. WATSON, G. N., A Treatise on the Theory of Bessel Functions, Cambridge University Press (1962). Zbl0174.36202MR1349110
23. WIENER, N., A class of gap theorems, Ann. Scuola Norm. Sup. Pisa (2), 3 (1934), 367-372. MR1556735
24. YOUNG, R. M., An Introduction to Nonharmonic Fourier Series, Academic Press (1980). Zbl0493.42001MR591684

1. Michel Mehrenberger, Critical length for a Beurling type theorem
2. Sergei Avdonin, Marius Tucsnak, Simultaneous controllability in sharp time for two elastic strings
3. Emmanuelle Crépeau, Christophe Prieur, Control of a clamped-free beam by a piezoelectric actuator
4. Sergei Avdonin, Marius Tucsnak, Simultaneous controllability in sharp time for two elastic strings
5. Sergei Avdonin, William Moran, Ingham-type inequalities and Riesz bases of divided differences
6. Paola Loreti, Exact controllability of shells in minimal time