Spectral properties of weakly almost periodic cosine functions

Valentina Casarino

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1998)

  • Volume: 9, Issue: 3, page 177-211
  • ISSN: 1120-6330

Abstract

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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.

How to cite

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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 9.3 (1998): 177-211. <http://eudml.org/doc/252430>.

@article{Casarino1998,
abstract = {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.},
author = {Casarino, Valentina},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Cosine functions; Asymptotically almost periodic applications; Dynamical systems; almost periodic functions; dynamical systems; spectral structure; infinitesimal generator; strongly continuous cosine function; ergodic properties of cosine functions},
language = {eng},
month = {9},
number = {3},
pages = {177-211},
publisher = {Accademia Nazionale dei Lincei},
title = {Spectral properties of weakly almost periodic cosine functions},
url = {http://eudml.org/doc/252430},
volume = {9},
year = {1998},
}

TY - JOUR
AU - Casarino, Valentina
TI - Spectral properties of weakly almost periodic cosine functions
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1998/9//
PB - Accademia Nazionale dei Lincei
VL - 9
IS - 3
SP - 177
EP - 211
AB - 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.
LA - eng
KW - Cosine functions; Asymptotically almost periodic applications; Dynamical systems; almost periodic functions; dynamical systems; spectral structure; infinitesimal generator; strongly continuous cosine function; ergodic properties of cosine functions
UR - http://eudml.org/doc/252430
ER -

References

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  1. Amerio, L. - Prouse, G., Almost periodic functions and functional equations. Van Nostrand, New York1971. Zbl0215.15701MR275061
  2. Arendt, W. - Batty, C. J. K., Asymptotically almost periodic solutions of inhomogeneous Cauchy problems on the half-line. To appear. Zbl0952.34048MR1673408DOI10.1112/S0024609398005657
  3. Arendt, W. - Batty, C. J. K., Almost periodic solutions of first and second order Cauchy problem. To appear. Zbl0879.34046MR1456602DOI10.1006/jdeq.1997.3266
  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-Tokyo1986. MR839450
  5. Banks, J. - Brooks, J. - Cairns, G. - Davis, G. - Stacey, P., On Devaney’s definition of chaos. Amer. Math. Monthly, 99, 1992, 332-334. Zbl0758.58019MR1157223DOI10.2307/2324899
  6. Bart, H. - Goldberg, S., Characterization of almost periodic strongly continuous groups and semigroups. Math. Ann., 236, 1978, 105-116. Zbl0365.47019MR493506
  7. Baskakov, A. G., Harmonic analysis of cosine and exponential operator-valued functions. Math. USSR Sb., 52, 1985, 63-90. Zbl0569.43004
  8. Bohr, H., Almost periodic functions. Chelsea, New York1947. Zbl0278.42019MR20163
  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. Zbl0921.42005MR1611609
  10. Cioranescu, I., Characterization of almost periodic strongly continuous cosine operator functions. Journal of Math. Anal. and Appl., 116, 1986, 222-229. Zbl0604.47026MR837349DOI10.1016/0022-247X(86)90054-5
  11. Fattorini, H., Uniformly bounded cosine functions in Hilbert space. Indiana. Univ. Math. J., 20, 1970, 411-425. Zbl0185.38501MR267417
  12. Fattorini, H., Second order linear differential equations. North-Holland, Amsterdam1985. Zbl0564.34063MR797071
  13. Fréchet, M., Les fonctions asymptotiquement presque-périodiques continues. C. R. Acad. Sci. Paris, 213, 1941, 520-522. MR9062JFM67.0231.01
  14. Giusti, E., Funzioni coseno periodiche. Boll. Unione Mat. Ital., 22, 1967, 478-485. Zbl0182.19304MR233237
  15. Goldstein, J. A., Semigroups of operators and applications. Oxford University Press, Oxford1985. Zbl0592.47034MR790497
  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. Zbl0393.47004MR487585
  17. Henriquez, H. R., On Stepanov-almost periodic semigroups and cosine functions of operators. Journal of Math. Anal. and Appl., 146, 1990, 420-433. Zbl0719.47023MR1043111DOI10.1016/0022-247X(90)90313-5
  18. Kallman, R. R. - Rota, G., On the inequality f 2 4 f ′′ f . In: O. Shisha (ed.), Inequalities II. Academic Press, New York1970, 187-192. Zbl0222.47009MR278059
  19. Lin, M., On the uniform ergodic theorem. Proc. of the Amer. Math. Soc., 43, 1974, 337-340. Zbl0252.47004MR417821
  20. Lin, M., On the uniform ergodic theorem II. Proc. of the Amer. Math. Soc., 46, 1974, 217-225. Zbl0291.47006MR417822
  21. Meyer, Y., Algebraic numbers and harmonic analysis. North-Holland, Amsterdam1972. Zbl0267.43001MR485769
  22. Nagy, B., On cosine operator functions in Banach spaces. Acta Sci. Math. (Szeged), 36, 1974, 281-290. Zbl0273.47008MR374995
  23. van Neerven, J. M. A. M., The Asymptotic Behaviour of Semigroups of Linear Operators. Birkhäuser Verlag, Basel1996. Zbl0905.47001MR1409370DOI10.1007/978-3-0348-9206-3
  24. Piskarev, S. I., Periodic and almost periodic cosine operator functions. Math. USSR Sb., 46, 1983, 391-402. Zbl0558.35002MR663150
  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. Zbl0666.46007MR944213DOI10.1002/mana.19881350102
  26. Shaw, S. Y., On W * -continuous cosine operator functions. Journal of Funct. Anal., 66, 1986, 73-95. Zbl0611.47037MR829378DOI10.1016/0022-1236(86)90082-0
  27. Vesentini, E., Introduction to continuous semigroups. Scuola Normale Superiore, Pisa1996. Zbl1068.47001MR1736550
  28. Vesentini, E., Spectral properties of weakly asymptotically almost periodic semigroups. Advances in Math., 128, 1997, 217-241. Zbl0882.22002MR1454398DOI10.1006/aima.1997.1613
  29. Vesentini, E., Periodicity and almost periodicity in Markov lattice semigroups. Ann. Scuola Normale, 26, Pisa1998, 829-839. Zbl1036.47500MR1655544
  30. Walters, P., An Introduction to Ergodic Theory. Springer-Verlag, New York1982. Zbl0299.28012MR648108

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