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# On complex perturbations of infinite band Schrödinger operators

### Abstract

Let $H_0=-\frac{d^2}{dx^2}+V_0$ be an infinite band Schrödinger operator on $L^2(\mathbb R)$ with a real-valued potential $V_0\in L^\infty(\mathbb R)$. We study its complex perturbation $H=H_0+V$, defined in the form sense, and obtain the Lieb-Thirring type inequ\-alities for the rate of convergence of the discrete spectrum of $H$ to the joint essential spectrum. The assumptions on $V$ vary depending on the sign of $Re V$.

Key words: Schrödinger operators, infinite-band spectrum, Lieb-Thirring type inequalities, relatively compact perturbations, resolvent identity.

### Article Information

 Title On complex perturbations of infinite band Schrödinger operators Source Methods Funct. Anal. Topology, Vol. 21 (2015), no. 3, 237-245 MathSciNet MR3521694 zbMATH 06630270 Milestones Received 29/01/2015 Copyright The Author(s) 2015 (CC BY-SA)

### Authors Information

L. Golinskii
Mathematics Division, Institute for Low Temperature Physics and Engineering, 47 Lenin ave., Kharkiv, 61103, Ukraine

S. Kupin
IMB, Universit´e Bordeaux 1, 351 cours de la Lib´eration, 33405 Talence Cedex, France

### Citation Example

L. Golinskii and S. Kupin, On complex perturbations of infinite band Schrödinger operators, Methods Funct. Anal. Topology 21 (2015), no. 3, 237-245.

### BibTex

@article {MFAT774,
AUTHOR = {Golinskii, L. and Kupin, S.},
TITLE = {On complex perturbations of infinite band Schrödinger operators},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {21},
YEAR = {2015},
NUMBER = {3},
PAGES = {237-245},
ISSN = {1029-3531},
MRNUMBER = {MR3521694},
ZBLNUMBER = {06630270},
URL = {http://mfat.imath.kiev.ua/article/?id=774},
}

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