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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 transformation d’Abel-Radon des courants localement résiduels

Bruno Fabre (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

After recalling the definitions of the Abel-Radon transformation of currents and of locally residual currents, we show that the Abel-Radon transform ℛ ( α ) of a locally residual current α remains locally residual. Then a theorem of P. Griffiths, G. Henkin and M. Passare (cf. [7], [9] and [10]) can be formulated as follows  :Let U be a domain of the grassmannian variety G ( p , N ) of complex p -planes in N , U * : = ∪ t ∈ U H t be the corresponding linearly p -concave domain of N , and α be a locally residual current of bidegree ( N , p ) ....

Sur les nombres de Lelong associés à l'image directe d'un courant positif fermé

Jean-Pierre Demailly (1982)

Annales de l'institut Fourier

Grâce à une formule de Jensen en plusieurs variables, on définit les nombres de Lelong généralisés d’un courant positif fermé relativement à un poids logarithmiquement plurisousharmonique. Les propriétés d’invariance de ces nombres par rapport aux morphismes analytiques permettent d’encadrer précisément les nombres de Lelong d’une image directe en faisant intervenir certaines multiplicités du morphisme. Une théorie analogue peut être développée pour l’étude de la croissance à l’infini d’un courant....

Une estimation des coefficients tangents d'un courant positif fermé dans un domaine de C3.

Philippe. Charpentier, Yves Dupain (1992)

Publicacions Matemàtiques

In this paper, we study the behaviour near the boundary of the complex tangent coefficients of a closed positive current in a bounded domain of C3 with C∞ boundary. Assuming that the current satisfies the Blaschke condition, we give a condition on the complex tangent coefficients which is better than the one which can be proved using the pseudo-distance introduced by A. Nagel, E. Stein and S. Wainger (in analogy with the case of domains in C2). Moreover, when the domain is supposed to be pseudoconvex,...

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