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On the Briançon-Skoda theorem on a singular variety

Mats Andersson, Håkan Samuelsson, Jacob Sznajdman (2010)

Annales de l’institut Fourier

Let Z be a germ of a reduced analytic space of pure dimension. We provide an analytic proof of the uniform Briançon-Skoda theorem for the local ring 𝒪 Z ; a result which was previously proved by Huneke by algebraic methods. For ideals with few generators we also get much sharper results.

On the Cauchy problem in a class of entire functions in several variables

Eugeni Leinartas (1996)

Banach Center Publications

We study the integral representation of solutions to the Cauchy problem for a differential equation with constant coefficients. The Cauchy data and the right-hand of the equation are given by entire functions on a complex hyperplane of n + 1 . The Borel transformation of power series and residue theory are used as the main methods of investigation.

On the dependence of the Bergman function on deformations of the Hartogs domain

Zbigniew Pasternak-Winiarski (1991)

Annales Polonici Mathematici

We apply the Rudin idea to represent the Bergman kernel of the Hartogs domain as the sum of a series of weighted Bergman functions in the study of the dependence of this kernel on deformations of the domain. We prove that the Bergman function depends smoothly on the function defining the Hartogs domain.

On the Djrbashian kernel of a Siegel domain

Elisabetta Barletta, Sorin 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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