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Poly-Bergman Projections and Orthogonal Decompositions of L2-spaces Over Bounded Domains

  • Yuri I. Karlovich
  • Luís V. Pessoa
Part of the Operator Theory: Advances and Applications book series (OT, volume 181)

Abstract

The paper is devoted to obtaining explicit representations of poly-Bergman and anti-poly-Bergman projections in terms of the singular integral operators S D and S D * on the unit disk D, studying relations between different true poly-Bergman and true anti-poly-Bergman spaces on the unit disk that are realized by the operators S D and S D * , establishing two new orthogonal decompositions of the space L 2(U, dA) (in terms of poly-Bergman and anti-poly-Bergman spaces) for an arbitrary bounded open set U ⊂ ℂ with the Lebesgue area measure dA, considering violation of Dzhuraev’s formulas and establishing explicit forms of the Bergman and anti-Bergman projections for several open sectors.

Keywords

Poly-Bergman and anti-poly-Bergman spaces and projections singular integral operators bounded domain Dzhuraev’s formulas orthogonal decomposition. 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • Yuri I. Karlovich
    • 1
  • Luís V. Pessoa
    • 2
  1. 1.Facultad de CienciasUniversidad Autónoma del Estado de MorelosCuernavaca, MorelosMéxico
  2. 2.Departamento de MatemáticaInstituto Superior TécnicoLisboaPortugal

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