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The Noether theory of singular integral functional operators with continuous coefficients on a non-closed contour

  • Victor G. Kravchenko
  • Georgii S. Litvinchuk
Chapter
  • 151 Downloads
Part of the Mathematics and Its Applications book series (MAIA, volume 289)

Abstract

In the preceding two chapters, the SIFO of first order
$$\mathcal{T} = \left( {a\left( t \right)I + b\left( t \right){{U}_{\alpha }}} \right){{P}_{ + }} + \left( {c\left( t \right)I + d\left( t \right){{U}_{\beta }}} \right){{P}_{ - }},t \in \Gamma$$
where ab c,d are scalar or matrix coefficients, was studied in the so-called continuous case, i.e., when the following three conditions are fulfilled simultaneously:
  1. 1

    \(a,b,c,d \in {C^{n \times n}}\left( \Gamma \right)\)

     
  2. 2

    \(\alpha ',\beta ' \in {H_\lambda }\left( \Gamma \right)\)

     
  3. 3

    Γ is a closed Lyapunov contour.

     

Keywords

Compact Operator Singular Integral Operator Index Formula Abstract Scheme Paired Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1994

Authors and Affiliations

  • Victor G. Kravchenko
    • 1
  • Georgii S. Litvinchuk
    • 2
  1. 1.Ukrainian State Hydrometeorological InstituteOdessaUkraine
  2. 2.Ukrainian State UniversityOdessaUkraine

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