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.
@article{BUMI_1999_8_2B_1_33_0, author = {Claudio Baiocchi and Vilmos Komornik and Paola Loreti}, title = {Ingham type theorems and applications to control theory}, journal = {Bollettino dell'Unione Matematica Italiana}, volume = {2-A}, year = {1999}, pages = {33-63}, zbl = {0924.42022}, mrnumber = {1794544}, language = {en}, url = {http://dml.mathdoc.fr/item/BUMI_1999_8_2B_1_33_0} }
Baiocchi, Claudio; Komornik, Vilmos; Loreti, Paola. Ingham type theorems and applications to control theory. Bollettino dell'Unione Matematica Italiana, Tome 2-A (1999) pp. 33-63. http://gdmltest.u-ga.fr/item/BUMI_1999_8_2B_1_33_0/
[1] 2, Birkhäuser (1989).
- (editors), The Collected Works of Arne Beurling, Volume[2] 45. Cambridge University Press, New York (1957). | MR 87708 | Zbl 0077.04801
, An Introduction to Diophantine Approximation, Cambridge Tracts in Mathematics - Mathematical Physics, No.[3] 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 1408769 | Zbl 0865.35075
- ,[4] Boundary value control of the wave equation in a spherical region, SIAM J. Control, 13 (1975), 174-196. | MR 355756 | Zbl 0315.93004
- ,[5] Séries lacunaires et contrôle semi-interne des vibrations d'une plaque rectangulaire, J. Math. Pures Appl., 68 (1989), 457-465. | MR 1046761 | Zbl 0685.93039
,[6] Some trigonometrical inequalities with applications in the theory of series, Math. Z., 41 (1936), 367-379. | MR 1545625 | Zbl 0014.21503
,[7] On a theorem of Ingham, J. Fourier Analysis, to appear. | MR 1491935 | Zbl 0939.42004
- - ,[8] Singular internal stabilization of the wave equation, J. Differential Equations, to appear. | MR 1620290 | Zbl 0920.35029
- - ,[9] Pseudo-périodicité et séries de Fourier lacunaires, Ann. Sci. de l'E.N.S., 79 (1962), 93-150. | MR 154060 | Zbl 0105.28601
,[10] 36, Masson-John Wiley, Paris-Chicester (1994). | MR 1359765 | Zbl 0937.93003
, Exact Controllability and Stabilization. The Multiplier Method, Collection RMA, Vol.[11] Observabilité frontière de systèmes couplés par analyse non harmonique vectorielle, C. R. Acad. Sci. Paris Sér. I Math., 324 (1997), 895-900. | MR 1450445 | Zbl 0880.93006
- ,[12] Ingham type theorems for vector-valued functions and observability of coupled linear systems, SIAM J. Control Optim., to appear. | MR 1655862 | Zbl 0963.93013
- ,[13] Observability of compactly perturbed systems, submitted. | Zbl 0952.34047
- ,[14] | MR 712486 | Zbl 0514.93001
, Contrôle des systèmes distribués singuliers, Gauthiers-Villars, Paris (1983).[15] Partial exact controllability for spherical membranes, SIAM J. Control Optim., 35 (1997), 641-653. | MR 1436643 | Zbl 0879.93002
- ,[16] Proof of a gap theorem, Duke Math. J., 4 (1938), 469-472. | MR 1546068
- ,[17] | MR 827223 | Zbl 0587.47036
, A Treatise on the Shift Operator, Springer, Berlin (1986).[18] 19, Amer. Math. Soc., New York (1934). | MR 1451142 | Zbl 0011.01601
- , Fourier Transforms in the Complex Domain, Amer. Math. Soc. Colloq. Publ., Vol.[19] 130 (1995), 131-160. | MR 1331980 | Zbl 0872.46006
, On the connection between exponential bases and certain related sequences in , J. Funct. Anal.,[20] On an inequality, Ann. Univ. Sci. Budapest. Eötvös Sect. Math., 1 (1959), 3-6. | MR 101445 | Zbl 0092.29001
,[21] Divided differences and systems of nonharmonic Fourier series, Proc. Amer. Math. Soc., 80 (1980), 47-57. | MR 574507 | Zbl 0448.42009
,[22] | MR 1349110 | Zbl 0174.36202
, A Treatise on the Theory of Bessel Functions, Cambridge University Press (1962).[23] A class of gap theorems, Ann. Scuola Norm. Sup. Pisa (2), 3 (1934), 367-372. | MR 1556735
, , An Introduction to Nonharmonic Fourier Series, Academic Press (1980).