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On the Djrbashian kernel of a Siegel domain

Elisabetta BarlettaSorin Dragomir — 1998

Studia Mathematica

We establish an inversion formula for the M. M. Djrbashian A. H. Karapetyan integral transform (cf. [6]) on the Siegel domain Ω n = ζ n : ϱ ( ζ ) > 0 , ϱ ( ζ ) = I m ( ζ 1 ) - | ζ ' | 2 . We build a family of Kähler metrics of constant holomorphic curvature whose potentials are the ϱ α -Bergman kernels, α > -1, (in the sense of Z. Pasternak-Winiarski [20] of Ω n . We build an anti-holomorphic embedding of Ω n in the complex projective Hilbert space ( H α 2 ( Ω n ) ) and study (in connection with work by A. Odzijewicz [18] the corresponding transition probability amplitudes....

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