Convolution Type Operators on ℝN

  • Vladimir Rabinovich
  • Bernd Silbermann
  • Steffen Roch
Part of the Operator Theory: Advances and Applications book series (OT, volume 150)


In this chapter, we are going to introduce a Banach algebra Bp of operators onLp(ℝ N ) which become band-dominated operators acting onlP(ℤ N ,X) withX= Lp([0, 1)N) after a suitable discretization and which are, thus, subject to the general theory developed in the previous chapter. Prominent members of this class are the Fourier convolution operators, certain pseudodifferential operators as well as operators in finite differences. We employ the close relationship between operators in Bpand their discretizations to study the local invertibility at infinity (which is related with the Fredholmness) as well as the applicability of the finite section method for operators in Bp.


Limit Operator Essential Spectrum Fredholm Operator Angular Point Operator Spectrum 
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Copyright information

© Springer Basel AG 2004

Authors and Affiliations

  • Vladimir Rabinovich
    • 1
  • Bernd Silbermann
    • 2
  • Steffen Roch
    • 3
  1. 1.Instituto Politécnico NacionalESIME ZacatencoMexico, D.F.USA
  2. 2.Department of MathematicsTechnical University of ChemnitzChemnitzGermany
  3. 3.Department of MathematicsTechnical University of DarmstadtDarmstadtGermany

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