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Hörmander systems and harmonic morphisms

Elisabetta Barletta — 2003

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Given a Hörmander system X = { X 1 , , X m } on a domain Ω 𝐑 n we show that any subelliptic harmonic morphism φ from Ω into a ν -dimensional riemannian manifold N is a (smooth) subelliptic harmonic map (in the sense of J. Jost & C-J. Xu, [9]). Also φ is a submersion provided that ν m and X has rank m . If Ω = 𝐇 n (the Heisenberg group) and X = 1 2 L α + L α ¯ , 1 2 i L α - L α ¯ , where L α ¯ = / z ¯ α - i z α / t is the Lewy operator, then a smooth map φ : Ω N is a subelliptic harmonic morphism if and only if φ π : ( C ( 𝐇 n ) , F θ 0 ) N is a harmonic morphism, where S 1 C ( 𝐇 n ) π 𝐇 n is the canonical circle bundle and F θ 0 is the Fefferman...

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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