Spectral properties of weakly almost periodic cosine functions
Casarino, Valentina
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 9 (1998), p. 177-211 / Harvested from Biblioteca Digitale Italiana di Matematica
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The spectral structure of the infinitesimal generator of a strongly continuous cosine function of linear bounded operators is investigated, under assumptions on the almost periodic behaviour of applications generated, in various ways, by C. Moreover, a first approach is presented to the analysis of connection between cosine functions and dynamical systems.

Si studia la struttura spettrale del generatore infinitesimale di una funzione coseno fortemente continua di operatori lineari limitati, sotto ipotesi sul comportamento quasi periodico di applicazioni generate, in diversi modi, da C. È, inoltre, presentato un primo approccio all’analisi del legame fra funzioni coseno e sistemi dinamici.

Publié le : 1998-09-01
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     author = {Valentina Casarino},
     title = {Spectral properties of weakly almost periodic cosine functions},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {9},
     year = {1998},
     pages = {177-211},
     zbl = {0944.47027},
     mrnumber = {1683008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_1998_9_9_3_177_0}
}

Casarino, Valentina. Spectral properties of weakly almost periodic cosine functions. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 9 (1998) pp. 177-211. http://gdmltest.u-ga.fr/item/RLIN_1998_9_9_3_177_0/

[1] Amerio, L. - Prouse, G., Almost periodic functions and functional equations. Van Nostrand, New York 1971. | MR 275061 | Zbl 0215.15701

[2] Arendt, W. - Batty, C. J. K., Asymptotically almost periodic solutions of inhomogeneous Cauchy problems on the half-line. To appear. | MR 1673408 | Zbl 0952.34048

[3] Arendt, W. - Batty, C. J. K., Almost periodic solutions of first and second order Cauchy problem. To appear. | MR 1456602 | Zbl 0879.34046

[4] Arendt, W. - Grabosch, A. - Greiner, G. - Groh, U. - Lotz, H. P. - Moustakas, U. - Nagel, R. - Neubrander, F. - Sclotterbeck, U., One-Parameter Semigroups of Positive Operators. Lecture Notes in Mathematics, n.1184, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo 1986. | MR 839450

[5] Banks, J. - Brooks, J. - Cairns, G. - Davis, G. - Stacey, P., On Devaney’s definition of chaos. Amer. Math. Monthly, 99, 1992, 332-334. | MR 1157223 | Zbl 0758.58019

[6] Bart, H. - Goldberg, S., Characterization of almost periodic strongly continuous groups and semigroups. Math. Ann., 236, 1978, 105-116. | MR 493506 | Zbl 0365.47019

[7] Baskakov, A. G., Harmonic analysis of cosine and exponential operator-valued functions. Math. USSR Sb., 52, 1985, 63-90. | Zbl 0569.43004

[8] Bohr, H., Almost periodic functions. Chelsea, New York1947. | MR 20163 | Zbl 0278.42019

[9] Casarino, V., Spectral properties of weakly asymptotically almost periodic semigroups in the sense of Stepanov. Rend. Mat. Acc. Lincei, s. 9, vol. 8, 1997, 167-181. | MR 1611609 | Zbl 0921.42005

[10] Cioranescu, I., Characterization of almost periodic strongly continuous cosine operator functions. Journal of Math. Anal. and Appl., 116, 1986, 222-229. | MR 837349 | Zbl 0604.47026

[11] Fattorini, H., Uniformly bounded cosine functions in Hilbert space. Indiana. Univ. Math. J., 20, 1970, 411-425. | MR 267417 | Zbl 0185.38501

[12] Fattorini, H., Second order linear differential equations. North-Holland, Amsterdam1985. | MR 797071 | Zbl 0564.34063

[13] Fréchet, M., Les fonctions asymptotiquement presque-périodiques continues. C. R. Acad. Sci. Paris, 213, 1941, 520-522. | JFM 67.0231.01 | MR 9062

[14] Giusti, E., Funzioni coseno periodiche. Boll. Unione Mat. Ital., 22, 1967, 478-485. | MR 233237 | Zbl 0182.19304

[15] Goldstein, J. A., Semigroups of operators and applications. Oxford University Press, Oxford1985. | MR 790497 | Zbl 0592.47034

[16] Goldstein, J. A. - Radin, C. - Showalter, R. E., Convergence rates of ergodic limits for semigroups and cosine functions. Semigroup Forum, 16, 1978, 89-95. | MR 487585 | Zbl 0393.47004

[17] Henriquez, H. R., On Stepanov-almost periodic semigroups and cosine functions of operators. Journal of Math. Anal. and Appl., 146, 1990, 420-433. | MR 1043111 | Zbl 0719.47023

[18] Kallman, R. R. - Rota, G., On the inequality f′2≤4⁢f′′⋅f. In: O. Shisha (ed.), Inequalities II. Academic Press, New York 1970, 187-192. | MR 278059 | Zbl 0222.47009

[19] Lin, M., On the uniform ergodic theorem. Proc. of the Amer. Math. Soc., 43, 1974, 337-340. | MR 417821 | Zbl 0252.47004

[20] Lin, M., On the uniform ergodic theorem II. Proc. of the Amer. Math. Soc., 46, 1974, 217-225. | MR 417822 | Zbl 0291.47006

[21] Meyer, Y., Algebraic numbers and harmonic analysis. North-Holland, Amsterdam1972. | MR 485769 | Zbl 0267.43001

[22] Nagy, B., On cosine operator functions in Banach spaces. Acta Sci. Math. (Szeged), 36, 1974, 281-290. | MR 374995 | Zbl 0273.47008

[23] Van Neerven, J. M. A. M., The Asymptotic Behaviour of Semigroups of Linear Operators. Birkhäuser Verlag, Basel1996. | MR 1409370 | Zbl 0905.47001

[24] Piskarev, S. I., Periodic and almost periodic cosine operator functions. Math. USSR Sb., 46, 1983, 391-402. | MR 663150 | Zbl 0558.35002

[25] Ruess, W. M. - Summers, W. H., Compactness in spaces of vector-valued continuous functions and asymptotic almost periodicity. Math. Nachr., 135, 1988, 7-33. | MR 944213 | Zbl 0666.46007

[26] Shaw, S. Y., On W*-continuous cosine operator functions. Journal of Funct. Anal., 66, 1986, 73-95. | MR 829378 | Zbl 0611.47037

[27] Vesentini, E., Introduction to continuous semigroups. Scuola Normale Superiore, Pisa1996. | MR 1736550 | Zbl 1068.47001

[28] Vesentini, E., Spectral properties of weakly asymptotically almost periodic semigroups. Advances in Math., 128, 1997, 217-241. | MR 1454398 | Zbl 0882.22002

[29] Vesentini, E., Periodicity and almost periodicity in Markov lattice semigroups. Ann. Scuola Normale, 26, Pisa1998, 829-839. | MR 1655544 | Zbl 1036.47500

[30] Walters, P., An Introduction to Ergodic Theory. Springer-Verlag, New York1982. | MR 648108 | Zbl 0299.28012