Skip to main content
Log in

General time-dependent bounded perturbation of a strongly continuous semigroup

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We consider an evolution family whose generator is formed by a time-dependent bounded perturbation of a strongly continuous semigroup. We do not use the condition of the continuity of a perturbation. We prove a formula for a variation of a parameter and the corresponding generalization of the Dyson-Phillips theorem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. T. Kato, “On linear differential equations in Banach spaces,” Commun. Pure Appl. Math., 9, 479–486 (1956).

    MATH  Google Scholar 

  2. K.-J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Springer, New York (2000).

    Google Scholar 

  3. E. Raebiger, A. Rhandi, and R. Schnaubelt, “Perturbation and an abstract characterization of evolution semigroups,” J. Math. Anal. Appl., 198, 516–533 (1996).

    Article  MathSciNet  Google Scholar 

  4. M. Hockman, “The abstract time-dependent Cauchy problem,” Trans. Amer. Math. Soc., 133, No. 1, 1–50 (1968).

    Article  MathSciNet  Google Scholar 

  5. I. I. Gikhman and A. V. Skorokhod, Theory of Random Processes [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  6. N. V. Kartashov, Strong Stable Markov Chains, VSP, Utrecht (1996).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 12, pp. 1625–1632, December, 2005.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kartashov, M.V. General time-dependent bounded perturbation of a strongly continuous semigroup. Ukr Math J 57, 1901–1910 (2005). https://doi.org/10.1007/s11253-006-0038-0

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-006-0038-0

Keywords

Navigation