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# On square root domains for non-self-adjoint Sturm-Liouville operators

### Abstract

We determine square root domains for non-self-adjoint Sturm-Liouville operators of the type $$L_{p,q,r,s} = - \frac{d}{dx}p\frac{d}{dx}+r\frac{d}{dx}-\frac{d}{dx}s+q$$ in $L^2((c,d);dx)$, where either $(c,d)$ coincides with the real line $\mathbb R$, the half-line $(a,\infty)$, $a \in \mathbb R$, or with the bounded interval $(a,b) \subset \mathbb R$, under very general conditions on the coefficients $q, r, s$. We treat Dirichlet and Neumann boundary conditions at $a$ in the half-line case, and Dirichlet and/or Neumann boundary conditions at $a,b$ in the final interval context. (In the particular case $p=1$ a.e. on $(a,b)$, we treat all separated boundary conditions at $a, b$.)

Key words: Square root domains, Kato problem, additive perturbations, Sturm–Liouville operators.

### Article Information

 Title On square root domains for non-self-adjoint Sturm-Liouville operators Source Methods Funct. Anal. Topology, Vol. 19 (2013), no. 3, 227-259 MathSciNet MR3136729 zbMATH 1289.47091 Milestones Received 10/05/2013; Revised: 14/06/2013 Copyright The Author(s) 2013 (CC BY-SA)

### Authors Information

Fritz Gesztesy
Department of Mathematics, University of Missouri, Columbia, MO 65211, USA

Steve Hofmann
Department of Mathematics, University of Missouri, Columbia, MO 65211, USA

Roger Nichols
Mathematics Department, The University of Tennessee at Chattanooga, 415 EMCS Building, Dept. 6956, 615 McCallie Ave, Chattanooga, TN 37403, USA

### Citation Example

Fritz Gesztesy, Steve Hofmann, and Roger Nichols, On square root domains for non-self-adjoint Sturm-Liouville operators, Methods Funct. Anal. Topology 19 (2013), no. 3, 227-259.

### BibTex

@article {MFAT697,
AUTHOR = {Gesztesy, Fritz and Hofmann, Steve and Nichols, Roger},
TITLE = {On square root domains for non-self-adjoint Sturm-Liouville operators},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {19},
YEAR = {2013},
NUMBER = {3},
PAGES = {227-259},
ISSN = {1029-3531},
MRNUMBER = {MR3136729},
ZBLNUMBER = {1289.47091},
URL = {http://mfat.imath.kiev.ua/article/?id=697},
}