Skip to main content
SpringerLink
Log in

On the spectral boundary value problems and boundary approximate controllability of linear systems

  • Published:
Rendiconti del Circolo Matematico di Palermo Aims and scope Submit manuscript

Abstract

The main subject of this paper is the study of a general spectral boundary value problems with right invertible (resp. left invertible) operators and corresponding initial boundary operators. The obtained results are used to describe the approximate boundary controllability of linear systems in abstract operator-theoretic setting.

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

Access this article

Log in via an institution

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. Amrein, W.O., Pearson, D.B.: \(M\)-operators: a generalization of Weyl-Titchmarsh theory. J. Comput. Appl. Math. 171, 1–26 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  2. Behrndt, J., Langer, M.: Boundary value problems for elliptic partial differential operators on bounded domains. J. Funct. Anal. 243, 536–565 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  3. Behrndt, J., Langer, M.: Elliptic operators, Dirichlet-to-Neumann maps and quasi boundary triples. London Math. Soc. Lect. Note Ser. 404, 121–160 (2012)

    MathSciNet  Google Scholar 

  4. Behrndt, J., Langer, M., Lotoreichik, V.: Trace formulae and singular values of resolvent power differences of self-adjoint elliptic operators. J. London Math. Soc. 88(2), 319–337 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  5. Browder, F.E.: On the spectral theory of elliptic differential operators I. Math. Ann. 142, 22–130 (1961)

    Article  MATH  MathSciNet  Google Scholar 

  6. Curtain, R.F.: In: Springer, H., Zwart J. (eds) An Introduction to Infinite-Dimensional Linear Systems Theory (1995)

  7. Hassi, S., de Snoo, H., Szafraniec, F. Operator methods for boundary value problems. London Math. Soc. Lect. Note Ser. 404 (2012).

  8. Lutgen, J.: On essential spectra of operator-matrices and their Feshbach maps. J. Math. Anal. Appl. 289, 419–430 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  9. Mau, N.V.: Boundary Value Problems and Controllability of Linear Systems with Right Invertible Operators. Dissertationes Mathematics, Warszawa (1992)

    Google Scholar 

  10. Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer, New York (1983)

    Book  MATH  Google Scholar 

  11. Przeworska-Rolewicz, D.: Algebraic Analysis. PWN and Reidel, Warszawa, Dordrecht (1988)

    Book  MATH  Google Scholar 

  12. Przeworska-Rolewicz, D.: Algebraic theory of right invertible operators. Studia Math. XLVIII, 129–144 (1973)

    MathSciNet  Google Scholar 

  13. Ryzhov, V.: Spectral boundary value problems and their linear operators. Opuscula Mathematica 27(2), 305–331 (2007)

    MATH  MathSciNet  Google Scholar 

  14. Ryzhov, V.: A note on an operator-theoretic approach to classic boundary value problems for harmonic and analytic functions in complex plane domains. Integr. Equ. Oper. Theory 67, 327–339 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  15. Staffans, O.J.: Well-Posed Linear Systems. Cambridge University Press, Cambridge (2005)

    Book  MATH  Google Scholar 

  16. Thi, H.V.: Approximate controllability for systems described by right invertible operators. Control Cybern 37(1), 39–51 (2008)

    Google Scholar 

  17. Zabczyk, J.: Mathematical Control Theory: An Introduction. Birkhauser, Boston (1992)

    MATH  Google Scholar 

Download references

Acknowledgments

The authors would like to thank the anonymous referee for their constructive comments and suggestions to improve the quality of the paper.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Tlemcen, Tlemcen, Algeria

    Nassima Khaldi

  2. Department of Mathematics and informatics, National Polytechnic School of Oran, BP 1523, El M’naouar-Oran, Oran, Algeria

    Mohammed Benharrat

  3. Department of Mathematics, University of Oran, BP 1524, El M’naouar-Oran, Oran, Algeria

    Bekkai Messirdi

Authors
  1. Nassima Khaldi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohammed Benharrat
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bekkai Messirdi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammed Benharrat.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Khaldi, N., Benharrat, M. & Messirdi, B. On the spectral boundary value problems and boundary approximate controllability of linear systems. Rend. Circ. Mat. Palermo 63, 141–153 (2014). https://doi.org/10.1007/s12215-014-0147-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12215-014-0147-9

Keywords

Mathematics Subject Classification (2000)

Search

Navigation