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Erschienen in:
2008 | OriginalPaper | Buchkapitel
Poly-Bergman Projections and Orthogonal Decompositions of L 2-spaces Over Bounded Domains
verfasst von : Yuri I. Karlovich, Luís V. Pessoa
Erschienen in: Operator Algebras, Operator Theory and Applications
Verlag: Birkhäuser Basel
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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.