Poly-Bergman Projections and Orthogonal Decompositions of L2-spaces Over Bounded Domains
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.
KeywordsPoly-Bergman and anti-poly-Bergman spaces and projections singular integral operators bounded domain Dzhuraev’s formulas orthogonal decomposition.
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