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Subharmonicity properties of the Bergman kernel and some other functions associated to pseudoconvex domains

Bo Berndtsson (2006)

Annales de l’institut Fourier

Let D be a pseudoconvex domain in ℂ t k × ℂ z n and let φ be a plurisubharmonic function in D . For each t we consider the n -dimensional slice of D , D t = { z ; ( t , z ) ∈ D } , let φ t be the restriction of φ to D t and denote by K t ( z , ζ ) the Bergman kernel of D t with the weight function φ t . Generalizing a recent result of Maitani and Yamaguchi (corresponding to n = 1 and φ = 0 ) we prove that log K t ( z , z ) is a plurisubharmonic function in D . We also generalize an earlier results of Yamaguchi concerning the Robin function and discuss similar results in the setting...

Subsets of Hardy-class zero sets in the ball.

Pascal J. Thomas (1990)

Publicacions Matemàtiques

We consider the problem of whether the union of complex hyperplanes can be a subset of a zero variety for the Hardy classes of the ball. A sufficient condition is found, consisting in a strong geometric separatedness requirement, together with a quantitative requirement slightly stronger than the necessary condition for Nevanlinna class zero varieties.

Sul teorema di Cauchy-Morera per le funzioni analitiche di più variabili complesse

Gaetano Fichera (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

A Cauchy-Morera theorem is proved for a function w of n complex variables, assuming only w ∈ L l ⁢ o ⁢ c 1 . A related result of Bochner, concerning continuous functions, is extended to a larger function class.

Sulle classi di Dolbeault di tipo ( 0 , n - 1 ) con singolarità in un insieme discreto

Paolo Zappa (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

This paper shows how some techniques used for the meromorphic functions of one variable can be used for the explicit construction of a solution to the Mittag-Leffler problem for Dolbeault classes of tipe ( 0 , n - 1 ) with singularities in a discrete set of 𝐂 𝐧 and T n (a n -dimensional complex torus). A generalisation is given for the Weierstrass ζ and the Legendre relations.

Sur la composition de séries formelles à croissance contrôlée

Augustin Mouze (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let F be a holomorphic map from ℂ s to ℂ s defined in a neighborhood of zero such that F ( 0 ) = 0 . If the jacobian determinant of F is not identically zero, P. M. Eakin and G. A. Harris proved the following result: any formal power series 𝒜 such that 𝒜 ∘ F is analytic is itself analytic. If the jacobian determinant of F is identically zero, they proved that the previous conclusion is no more true. J. Chaumat and A.-M. Chollet extended this result in the case of formal power series satisfying growth conditions, of...

Sur la transformation de Fourier-Laurent dans un groupe analytique complexe réductif

Michel Lassalle (1978)

Annales de l'institut Fourier

Soit H un groupe analytique compact : son complexifié universel G est un groupe analytique complexe réductif. On introduit dans G une classe de “domaines de Reinhardt généralisés”, bi-invariants par H et caractérisés par une “base”, définie dans une sous-algèbre abélienne maximale de l’algèbre de Lie du groupe H et invariante par le groupe de Weyl.On donne une caractérisation par leurs coefficients de Fourier-Laurent des fonctions holomorphes dans un tel domaine. On montre que l’enveloppe d’holomorphie...

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