Open Access

A spectral analysis of some indefinite differential operators


Abstract

We investigate the main spectral properties of quasi-Hermitian extensions of the minimal symmetric operator $L_{\rm min}$ generated by the differential expression $-\frac{{\rm sgn}\, x}{|x|^{\alpha}}\frac{d^2}{dx^2} \ (\alpha>-1)$ in $L^2(\mathbb R, |x|^{\alpha})$. We describe their spectra, calculate the resolvents, and obtain a similarity criterion to a normal operator in terms of boundary conditions at zero. As an application of these results we describe the main spectral properties of the operator $\frac{{\rm sgn}\, x}{|x|^\alpha}\left( -\frac{d^2}{dx^2}+c \delta \right), \, \alpha>-1$.


Full Text





Article Information

TitleA spectral analysis of some indefinite differential operators
SourceMethods Funct. Anal. Topology, Vol. 12 (2006), no. 2, 157-169
MathSciNet MR2238037
CopyrightThe Author(s) 2006 (CC BY-SA)

Authors Information

A. S. Kostenko
Department of Mathematics, Donets'k National University, 24 Universitets'ka, Donets'k, 83055, Ukraine 


Google Scholar Metrics

Citing articles in Google Scholar
Similar articles in Google Scholar

Export article

Save to Mendeley



Citation Example

A. S. Kostenko, A spectral analysis of some indefinite differential operators, Methods Funct. Anal. Topology 12 (2006), no. 2, 157-169.


BibTex

@article {MFAT343,
    AUTHOR = {Kostenko, A. S.},
     TITLE = {A spectral analysis of some indefinite differential operators},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {12},
      YEAR = {2006},
    NUMBER = {2},
     PAGES = {157-169},
      ISSN = {1029-3531},
       URL = {http://mfat.imath.kiev.ua/article/?id=343},
}


All Issues