Trace formulae for Schrödinger operators with complex-valued potentials on cubic lattices

Trace formulae for Schrödinger operators with complex-valued potentials on cubic lattices

Abstract We consider a class of Schrödinger operators with complex decaying potentials on the lattice. Using some classical results from complex analysis we obtain some trace formulae and use them to estimate zeros of the Fredholm determinant in terms of the potential.

Bibliographic Details
Main Authors: Evgeny Korotyaev, Ari Laptev
Format: Article
Language:English
Published: World Scientific Publishing 2018-03-01
Series:Bulletin of Mathematical Sciences
Subjects:
Scattering
Trace formula
Lattice
Complex eigenvalues
Hardy spaces
Online Access:http://link.springer.com/article/10.1007/s13373-018-0117-1
Description
Summary:Abstract We consider a class of Schrödinger operators with complex decaying potentials on the lattice. Using some classical results from complex analysis we obtain some trace formulae and use them to estimate zeros of the Fredholm determinant in terms of the potential.
ISSN:1664-3607
1664-3615

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