Skip to main content
SpringerLink
Log in

Inverse Problem on the Entire Line and Some Connected Questions of Spectral Theory

  • Conference paper
Inverse and Algebraic Quantum Scattering Theory

Part of the book series: Lecture Notes in Physics ((LNP,volume 488))

  • 338 Accesses

Abstract

In this paper we consider several separate questions for one-dimensional-Schrödinger operators on the entire line. The paper consists of an Introduction, seven short Sections and three Appendices. Each of these Sections and Appendices is almost independent.

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 69.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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. H. Weyl, Ober gewöhnliche Differentialgleichungen mit Singularitäten und die zugehörigen Entwicklungen willkiirlicher Funktionen. Math. Ann. 68 (1910), 220–269.

    Article  MATH  MathSciNet  Google Scholar 

  2. C. E. Titchmarsh, Eigenfunctions expansions associated with second order differential equations. Part I, Oxford 1946.

    Google Scholar 

  3. B. M. Levitan, Inverse Sturm-Liouville problems. Utrecht, 1987.

    Google Scholar 

  4. F. S. Rofe-Beketov, The spectral matrix and the inverse Sturm-Liouville problem on the axis (−∞, ∞) Theorya Funktsiy, Funkts. Anal. Prilozhenija, 4, (1967), 189–197.

    MATH  MathSciNet  Google Scholar 

  5. B. M. Levitan, Some Special Tauberian Theorems for Fourier Type Integrals and Eigenfunction Expansion of Sturm-Liouville Equation on the Whole Line. Math. Nachr. 176 (1995), 179–193.

    Article  MATH  MathSciNet  Google Scholar 

  6. B. M. Levitan, The inverse Sturm-Liouville problem for finite-zone and infinite-zone potentials. Trudy Mosk. Obshch. 45, (1982), 3–36.

    MATH  MathSciNet  Google Scholar 

  7. S. P. Novikov: A periodic problem for Korteveg-de-Vries equation. Funct. Anal. Prilojenije, 8 (3) (1974) 236–240

    MATH  Google Scholar 

  8. P. Lax, Periodic solutions of the KdV equation. Comm.Pure Appl. Math. 28 (1975), 141–188.

    Article  MATH  MathSciNet  Google Scholar 

  9. J. Moser, Integrable Hamiltonian Systems and Spectral Theory. Accad. Naz. Lincei, Pisa (1981).

    Google Scholar 

  10. B. M. Levitan, On the asymptotic behaviour of the spectral function of a self-adjoint differential equation of second order. Izv. Akad. Nauk SSSR, Serie Math. 16 (1952), 325–352.

    MATH  MathSciNet  Google Scholar 

  11. B. M. Levitan, English translation: Amer. Math. Soc. Transi. (2) 101 (1973), 192–221.

    MATH  Google Scholar 

  12. B. M. Levitan and I. S. Sargsjan Introduction to Spectral Theory. Transi. of Math. Monographs, Amer. Math. Soc. (1975)

    Google Scholar 

  13. B. A. Dubrovin, Periodic problems for the Korteveg-de-Vries egation in the class of finite-band potentials. Funt. Anal. Appl. 9 (1975), 215–223.

    Article  Google Scholar 

  14. H, McKean and P. Moerbek, The spectrum of Hill’s equation. Invent. Math. 30 (3) (1975) 217–274.

    Article  ADS  MATH  MathSciNet  Google Scholar 

  15. B. M. Levitan: On a special Tauberian theorem. Izv. Akad. Nauk SSSR, Ser. Mat. 17 (1953), 269–284

    MATH  MathSciNet  Google Scholar 

  16. B. M. Levitan: English translation:Amer. Math. Soc. Transi. (2) (101) (1973), 222–238.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Minnesota, USA

    B. M. Levitan

Authors
  1. B. M. Levitan
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Theoretical Physics, Technical University of Budapest, Budafoki u. 8., 1521, Budapest, Hungary

    Barnabás Apagyi  & Péter Lévay  & 

  2. Computer Center of Eötvös University, ELTE, Budapest, Hungary

    Gábor Endrédi

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Levitan, B.M. (1997). Inverse Problem on the Entire Line and Some Connected Questions of Spectral Theory. In: Apagyi, B., Endrédi, G., Lévay, P. (eds) Inverse and Algebraic Quantum Scattering Theory. Lecture Notes in Physics, vol 488. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-14145-8_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-14145-8_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-14147-2

  • Online ISBN: 978-3-662-14145-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation