Lieb--Thirring bounds for complex Jacobi matrices
L. Golinskii, S. Kupin
TL;DR
This paper extends Lieb--Thirring bounds to complex Jacobi matrices in multiple dimensions, using a general method based on the Fan-Mirski Lemma, broadening the scope of spectral bounds in complex matrix analysis.
Contribution
It introduces new Lieb--Thirring bounds for complex Jacobi matrices in multiple dimensions, employing a novel approach based on the Fan-Mirski Lemma.
Findings
Derived various Lieb--Thirring bounds for complex Jacobi matrices
Method based on Fan-Mirski Lemma is broadly applicable
Extends classical bounds to complex and multi-dimensional cases
Abstract
We obtain various versions of classical Lieb--Thirring bounds for one- and multi-dimensional complex Jacobi matrices. Our method is based on Fan-Mirski Lemma and seems to be fairly general.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Matrix Theory and Algorithms · Quantum Mechanics and Non-Hermitian Physics