Integral Equations and Operator Theory

, Volume 37, Issue 2, pp 169–207 | Cite as

Relations between convolution type operators on intervals and on the half-line

  • L. P. Castro
  • F. O. Speck
Article
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Abstract

This paper is devoted to the question to obtain (algebraic and topologic) equivalence (after extension) relations between convolution type operators on unions of intervals and convolution type operators on the half-line. These operators are supposed to act between Bessel potential spaces,H s,p , which are the appropriate spaces in several applications. The present approach is based upon special properties of convenient projectors, decompositions and extension operators and the construction of certain homeomorphisms between the kernels of the projectors. The main advantage of the method is that it provides explicit operator matrix identities between the mentioned operators where the relations are constructed only by bounded invertible operators. So they are stronger than the (algebraic) Kuijper-Spitkovsky relation and the Bastos-dos Santos-Duduchava relation with respect to the transfer of properties on the prize that the relations depend on the orders of the spaces and hold only for non-critical orders:S − 1/p ∉ ℤ. For instance, (generalized) inverses of the operators are explicitly represented in terms of operator matrix factorization. Some applications are presented.

AMS Classification Numbers

47B35 45E10 47A20 47A05 46E35 47A68 78A45 
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Copyright information

© Birkhäuser Verlag 2000

Authors and Affiliations

  • L. P. Castro
    • 1
  • F. O. Speck
    • 2
  1. 1.Departamento de MatemáticaUniversidade de AveiroAveiroPortugal
  2. 2.Departamento de MatemáticaInstituto Superior TécnicoLisboa CodexPortugal

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