On non-selfadjoint perturbations of infinite band Schr\"odinger operators and Kato method

L. Golinskii; S. Kupin

On non-selfadjoint perturbations of infinite band Schr\"odinger operators and Kato method

Spectral Theory 2015-10-14 v1 Functional Analysis

Authors: L. Golinskii , S. Kupin

Abstract

Let $H_0=-\dd+V_0$ be a multidimensional Schr\"odinger ope\-rator with a real-valued potential and infinite band spectrum, and $H=H_0+V$ be its non-selfadjoint perturbation defined with the help of Kato approach. We prove Lieb--Thirring type inequalities for the discrete spectrum of $H$ in the case when $V_0\in L^\infty(\br^d)$ and $V\in L^p(\br^d)$ , $p>\max(d/2, 1)$ .

Keywords

non-selfadjoint perturbation Schrödinger operator infinite band spectrum Kato method Lieb-Thirring inequality discrete spectrum spectral theory

Cite

@article{arxiv.1510.03639,
  title  = {On non-selfadjoint perturbations of infinite band Schr\"odinger operators and Kato method},
  author = {L. Golinskii and S. Kupin},
  journal= {arXiv preprint arXiv:1510.03639},
  year   = {2015}
}

Comments

12 pages, 1 figure. arXiv admin note: text overlap with arXiv:1502.06022

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