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

Authors

  • J. Murphy </span>Mathematics Department, The University of Tennessee at Chattanooga, 415 EMCS Building, Dept. 6956, 615 McCallie Ave, Chattanooga, TN 37403, USA
  • R. Nichols </span>Mathematics Department, The University of Tennessee at Chattanooga, 415 EMCS Building, Dept. 6956, 615 McCallie Ave, Chattanooga, TN 37403, USA

DOI:

Keywords:

Coupled boundary conditions, Schrödinger operator, spectral shift function, vague convergence, weak convergence

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.

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Published

2017-12-25

Issue

Vol. 23 No. 4 (2017)

Section

Articles

How to Cite

Murphy, J., and R. Nichols. “Weak and Vague Convergence of Spectral Shift Functions of One-Dimensional Schrödinger Operators With Coupled Boundary Conditions”. Methods of Functional Analysis and Topology, vol. 23, no. 4, Dec. 2017, pp. 378-03, https://zen.imath.kiev.ua/index.php/mfat/article/view/678.