Publication Cover
Applicable Analysis
An International Journal
Volume 86, 2007 - Issue 10
40
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Sturm–Liouville operators in the half axis with shifted potentials

&
Pages 1211-1221 | Received 21 Mar 2007, Accepted 29 May 2007, Published online: 21 Sep 2010

References

  • Coddington , EA and Levinson , N . 1955 . “ Theory of ordinary differential equations ” . In International Series in Pure and Applied Mathematics , New York : McGraw–Hill Book Company Inc .
  • del Rio , R , Simon , B and Stolz , G . 1994 . Stability of spectral types for Sturm–Liouville operators . Mathematical Research Letters , 1 : 437 – 450 .
  • del Rio , R and Tchebotareva , O . 2007 . Sturm–Liouville operators in the half axis with local perturbations . Journal of Mathematical Analysis and Applications , 329 : 557 – 566 .
  • Hartman , P . 1982 . Ordinary Differential Equations , Boston : Birkhäuser .
  • Javrjan , VA . 1971 . A certain inverse problem for Sturm–Liouville operators . Izvestija Akademiya Nauk Aemjan SSR Ser. Mat. , 6 : 246 – 251 .
  • Kirsch , W , Molchanov , SA and Pastur , LA . 1990 . One-dimensional Schrödinger operators with unbounded potential: the pure point spectrum . Functional Analysis and its Applications , 24 : 176 – 186 .
  • Kirsch , W , Molchanov , SA and Pastur , LA . 1992 . “ One-dimensional Schrödinger operators with high potential barriers ” . In Operator Theory: Advances and Applications Vol. 57 , 163 – 170 . Basel Birkhäuser–Verlag
  • Kiselev , A , Last , Y and Simon , B . 2003 . Stability of singular spectral types under decaying perturbations . Journal of Functional Analysis , 198 : 1 – 27 .
  • Kotani , S . 1986 . Lyapunov exponents and spectra for one–dimensional Schrödinger operators . Contemporary Mathematics , 50 : 277 – 286 .
  • Kotani , S and Simon , B . 1987 . Localization in general one–dimensional random systems . Communications in Mathematical Physics , 112 : 103 – 119 .
  • Pearson , DB . 1993 . Value distribution and spectral analysis of differential operators . Journal of Physics A , 26 : 4067 – 4080 .
  • Simon , B and Wolff , T . 1986 . Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians . Communications on Pure and Applied Mathematics , 39 : 75 – 90 .
  • Stolz , G . 1995 . Localization for random Schrödinger operators with Poisson potential . Annales de l’Institut Henri Poincaré , 63 ( 3 ) : 297 – 314 .
  • Stolz , G . 1994 . Spectral Theory of Schrödinger Operators with Potentials of Infinite Barriers Type , Frankfurt am Main : Habilitationsschrift, Frankfurt University .
  • Weidmann , J . 1987 . Spectral Theory of Ordinary Differential Operators , Vol : Lectures Notes in Mathematics . 1258.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.