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.

Full Text

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},
}