Periodica Mathematica Hungarica

, Volume 14, Issue 1, pp 101–105 | Cite as

Über Die Konvergenz Operatorwertiger Cosinusfunktionen mit Gestörtem Infinitesimalen Erzeuger



On convergence of operator cosine functions with perturbed infinitesimal generator. The question under what kind of perturbations a closed linear operatorA remains of the class of infinitesimal generators of operator cosine functions seems to be a rather difficult one and is unsolved in general. In this note we give bounds for the perturbation of operator cosine functions caused byA-bounded perturbationsT ofA under the assumption thatT + A is also a generator.

AMS (MOS) subject classifications (1980)

Primary 34G10, 39B70 Secondary 47D05 

Key words and phrases

Operator-valued cosine functions second order differential equations in abstract spaces 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    H. O. Fattorini, Ordinary differential equations in linear topological spaces, I,J. Differential Equations 5 (1968), 72–105.MR 43 # 3593Google Scholar
  2. [2]
    H. O. Fattorini, Ordinary differential equations in linear topological spaces, II,J. Differential Equations 6 (1969), 50–70.MR 43 # 3594Google Scholar
  3. [3]
    T. Kato,Perturbation theory for linear operators (second edition), Springer, Berlin, 1976.MR 53 # 11389Google Scholar
  4. [4]
    D. Lutz, On resolvents of generators of operator cosine functions.Google Scholar
  5. [5]
    B. Nagy, On cosine operator functions in Banach spaces,Acta Sci. Math. (Szeged)36 (1974), 281–289.MR 51 # 11191Google Scholar
  6. [6]
    M. Sova,Cosine operator functions, Rozprawy Mat. 49., 1966, 47 pp.MR 33 # 1745Google Scholar
  7. [7]
    T. Takenaka undN. Okazawa, A Phillips—Miyadera type perturbation theorem for cosine functions of operators,Tôkohu Math. J. 30 (1978), 107–115.MR 57 # 10497Google Scholar
  8. [8]
    C. C. Travis undF. G. Webb, Compactness, regularity, and uniform continuity properties of strongly continuous cosine families,Houston J. Math. 3 (1977), 555–567.MR 58 # 17957Google Scholar

Copyright information

© Akadémiai Kiadó 1983

Authors and Affiliations

  • D. Lutz
    • 1
  1. 1.Fachbereich 6 (Mathematik)Universität EssenEssenFederal Republic of Germany

Personalised recommendations