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Fredholm theory connected with a Douglis-Nirenberg system of differential equations over $\mathbb{R}^n$


Abstract

We consider a spectral problem over $\mathbb{R}^n$ for a Douglis-Nirenberg system of differential operators under limited smoothness assumptions and under the assumption of parameter-ellipticity in a closed sector $\mathcal{L}$ in the complex plane with vertex at the origin. We pose the problem in an $L_p$ Sobolev-Bessel potential space setting, $1 < p < \infty$, and denote by $A_p$ the operator induced in this setting by the spectral problem. We then derive results pertaining to the Fredholm theory for $A_p$ for values of the spectral parameter $\lambda$ lying in $\mathcal{L}$ as well as results pertaining to the invariance of the Fredholm domain of $A_p$ with $p$.

Key words: Parameter-ellipticity, Douglis-Nirenberg system, Fredholm properties.


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Article Information

TitleFredholm theory connected with a Douglis-Nirenberg system of differential equations over $\mathbb{R}^n$
SourceMethods Funct. Anal. Topology, Vol. 22 (2016), no. 4, 330-345
MathSciNet MR3591084
MilestonesReceived 27/04/2016
CopyrightThe Author(s) 2016 (CC BY-SA)

Authors Information

M. Faierman
School of Mathematics and Statistics, The University of New South Wales, UNSW Sydney, NSW 2052, Australia


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M. Faierman, Fredholm theory connected with a Douglis-Nirenberg system of differential equations over $\mathbb{R}^n$, Methods Funct. Anal. Topology 22 (2016), no. 4, 330-345.


BibTex

@article {MFAT913,
    AUTHOR = {Faierman, M.},
     TITLE = {Fredholm theory connected with a Douglis-Nirenberg system of differential equations over $\mathbb{R}^n$},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {22},
      YEAR = {2016},
    NUMBER = {4},
     PAGES = {330-345},
      ISSN = {1029-3531},
       URL = {http://mfat.imath.kiev.ua/article/?id=913},
}


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