Open Access

Weak and vague convergence of spectral shift functions of one-dimensional Schrödinger operators with coupled boundary conditions


Abstract

We prove weak and vague convergence results for spectral shift functions associated with self-adjoint one-dimensional Schrödinger operators on intervals of the form $(-\ell,\ell)$ to the full-line spectral shift function in the limit $\ell\to \infty$ for a class of coupled boundary conditions. The boundary conditions considered here include periodic boundary conditions as a special case.

Key words: Coupled boundary conditions, Schrödinger operator, spectral shift function, vague convergence, weak convergence.


Full Text





Article Information

TitleWeak and vague convergence of spectral shift functions of one-dimensional Schrödinger operators with coupled boundary conditions
SourceMethods Funct. Anal. Topology, Vol. 23 (2017), no. 4, 378-403
MilestonesReceived 07/04/2017
CopyrightThe Author(s) 2017 (CC BY-SA)

Authors Information

John Murphy
Mathematics Department, The University of Tennessee at Chattanooga, 415 EMCS Building, Dept. 6956, 615 McCallie Ave, Chattanooga, TN 37403, USA

Roger Nichols
Mathematics Department, The University of Tennessee at Chattanooga, 415 EMCS Building, Dept. 6956, 615 McCallie Ave, Chattanooga, TN 37403, USA


Google Scholar Metrics

Citing articles in Google Scholar
Similar articles in Google Scholar

Export article

Save to Mendeley



Citation Example

John Murphy and Roger Nichols, Weak and vague convergence of spectral shift functions of one-dimensional Schrödinger operators with coupled boundary conditions, Methods Funct. Anal. Topology 23 (2017), no. 4, 378-403.


BibTex

@article {MFAT1005,
    AUTHOR = {John Murphy and Roger Nichols},
     TITLE = {Weak and vague convergence of spectral shift functions of one-dimensional Schrödinger operators with coupled boundary conditions},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {23},
      YEAR = {2017},
    NUMBER = {4},
     PAGES = {378-403},
      ISSN = {1029-3531},
       URL = {http://mfat.imath.kiev.ua/article/?id=1005},
}


References

Coming Soon.

All Issues