Skip to main content
SpringerLink
Log in

A Factorization Model for the Generalized Friedrichs Extension in a Pontryagin Space

  • Conference paper
Book cover Operator Theory in Krein Spaces and Nonlinear Eigenvalue Problems

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 162))

Abstract

An operator model for the generalized Friedrichs extension in the Pontryagin space setting is presented. The model is based on a factorization of the associated Weyl function (or Q-function) and it carries the information on the asymptotic behavior of the Weyl function at z = ∞.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. V.A. Derkach, “On generalized resolvents of Hermitian relations”, J. Math. Sciences, 97 (1999), 4420–4460.

    MATH  MathSciNet  Google Scholar 

  2. V.A. Derkach and S. Hassi, “A reproducing kernel space model for Nκ-functions”, Proc. Amer. Math. Soc., 131 (2003), 3795–3806.

    Article  MathSciNet  Google Scholar 

  3. V.A. Derkach, S. Hassi, M.M. Malamud, and H.S.V. de Snoo, “Generalized resolvents of symmetric operators and admissibility”, Methods of Functional Analysis and Topology, 6 (2000), 24–55.

    MathSciNet  Google Scholar 

  4. V.A. Derkach, S. Hassi, and H.S.V. de Snoo, “Operator models associated with Kac subclasses of generalized Nevanlinna functions”, Methods of Functional Analysis and Topology, 5 (1999), 65–87.

    MathSciNet  Google Scholar 

  5. V.A. Derkach, S. Hassi, and H.S.V. de Snoo, “Generalized Nevanlinna functions with polynomial asymptotic behaviour and regular perturbations”, Oper. Theory Adv. Appl., 122 (2001), 169–189.

    Google Scholar 

  6. V.A. Derkach, S. Hassi, and H.S.V. de Snoo, “Operator models associated with singular perturbations”, Methods of Functional Analysis and Topology, 7 (2001), 1–21.

    Google Scholar 

  7. V.A. Derkach, S. Hassi, and H.S.V. de Snoo, “Rank one perturbations in a Pontryagin space with one negative square”, J. Funct. Anal., 188 (2002), 317–349.

    Article  MathSciNet  Google Scholar 

  8. V.A. Derkach, S. Hassi, and H.S.V. de Snoo, “Asymptotic expansions of generalized Nevanlinna functions and their spectral properties”, submitted.

    Google Scholar 

  9. V.A. Derkach and M.M. Malamud, “The extension theory of hermitian operators and the moment problem”, J. Math. Sciences, 73 (1995), 141–242.

    MathSciNet  Google Scholar 

  10. A. Dijksma, H. Langer, A. Luger, and Yu. Shondin, “A factorization result for generalized Nevanlinna functions of the class Nκ”, Integral Equations and Operator Theory, 36 (2000), 121–125.

    Article  MathSciNet  Google Scholar 

  11. A. Dijksma, H. Langer, A. Luger, and Yu. Shondin, “Minimal realizations of scalar generalized Nevanlinna functions related to their basic factorization”, Oper. Theory Adv. Appl., 154 (2004), 69–90.

    MathSciNet  Google Scholar 

  12. A. Dijksma, H. Langer, Yu.G. Shondin, and C. Zeinstra, “Self-adjoint operators with inner singularities and Pontryagin spaces”, Oper. Theory Adv. Appl., 118 (2000), 105–175.

    MathSciNet  Google Scholar 

  13. P. Jonas, H. Langer, and B. Textorius, “Models and unitary equivalence of cyclic selfadjoint operators in Pontryagin spaces”, Oper. Theory Adv. Appl., 59 (1992), 252–284.

    MathSciNet  Google Scholar 

  14. M.G. Krein and H. Langer, “Über die Q-Funktion eines π-hermiteschen Operators im Raume Πκ”, Acta. Sci. Math. (Szeged), 34 (1973), 191–230.

    MathSciNet  Google Scholar 

  15. M.G. Krein and H. Langer, “Über einige Fortsetzungsprobleme, die eng mit der Theorie hermitescher Operatoren im Raume Πκ zusammenhängen. I. Einige Funktionenklassen und ihre Darstellungen”, Math. Nachr., 77 (1977), 187–236.

    MathSciNet  Google Scholar 

  16. M.G. Krein and H. Langer, “Some propositions on analytic matrix functions related to the theory of operators in the space Πκ”, Acta Sci. Math. (Szeged), 43 (1981), 181–205.

    MathSciNet  Google Scholar 

  17. H. Langer, “A characterization of generalized zeros of negative type of functions of the class Nκ”, Oper. Theory Adv. Appl., 17 (1986), 201–212.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Donetsk National University, Universitetskaya str. 24, 83055, Donetsk, Ukraine

    Vladimir Derkach

  2. Department of Mathematics and Statistics, University of Vaasa, P.O. Box 700, 65101, Vaasa, Finland

    Seppo Hassi

  3. Department of Mathematics and Computing Science, University of Groningen, P.O. Box 800, 9700 AV, Groningen, Nederland

    Henk de Snoo

Authors
  1. Vladimir Derkach
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Seppo Hassi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Henk de Snoo
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Mathematik, Technische Universität Berlin, D-10623, Berlin, Germany

    Karl-Heinz Förster  & Peter Jonas  & 

  2. Institut für Analysis und Scientific Computing, Technische Universität Wien, A-1040, Wien, Austria

    Heinz Langer

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Birkhäuser Verlag Basel/Switzerland

About this paper

Cite this paper

Derkach, V., Hassi, S., de Snoo, H. (2005). A Factorization Model for the Generalized Friedrichs Extension in a Pontryagin Space. In: Förster, KH., Jonas, P., Langer, H. (eds) Operator Theory in Krein Spaces and Nonlinear Eigenvalue Problems. Operator Theory: Advances and Applications, vol 162. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7453-5_7

Download citation

Publish with us

Policies and ethics

Search

Navigation