Invariance of generalized L-regularity under holomorphic mappings

• Autorzy: Hecart J.
• Języki publikacji: EN

Abstrakty

EN

We show an invariance property for generalized L-regular sets (that is regular sets with respect to the generalized pluricomplex Green function defined in parabolic complex spaces) under holomorphic mappings.

Słowa kluczowe

EN

analytic spaces; generalized Green function; holomorphic mappings

PL

funkcja Greena; odwzorowanie holomorficzne; przestrzeń analityczna

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2000
• Tom: Vol. 48, no 2
• Strony: 187--192
• Opis fizyczny: Bibliogr. 11 poz.,

Twórcy

autor

Hecart J.

• Université Paul Sabatier, Laboratoire de Mathématiques E. Picard, UMR CNRS 5580, 118 Route de Narbonne, 31062 Toulouse Cedex, France

Bibliografia

• [1] E. Bedford, The operator (der on complex spaces, Séminaire d'analyse Lelong-Skoda, Lect. Notes Math., 919 (1981) 294-324.
• [2] H. Grauert, R. Remmert, Coherent analytic sheaves, Ser. Comprehensive Stud. Math. 265, Springer-Verlag, Berlin, Heidelberg 1984.
• [3] R. C. Gunning, Introduction to holomorphic functions of several variables: vol. II, Local theory, Mathematics Series, Wadsworth and Brooks/Cole, 1990.
• [4] M. Klimek, Pluripotential theory, London Math. Soc. Monogr. 6, Clarendon Press, Oxford 1991.
• [5] T. V. Nguyen, W. Pleśniak, Invariance of L-regularity and Leja's polynomial condition under holomorphic mappings, Proc. Roy. Irish Acad. Sect. A, 84 (2) (1984) 111-115.
• [6] W. Pleśniak, Invariance of the L-regularity of compact sets in Cn under holomorphic mappings, Trans. Amer. Math. Soc., 246 (1978) 373-383.
• [7] W. Stoll, Value distribution theory, Lect. Notes Math., Springer-Verlag, 600 (1977).
• [8] A. Zériahi, Fonction de Green pluricomplexe à pôle à l'infini sur un espace de Stein parabolique et applications, Math. Scand., 69 (1991) 89-126.
• [9] A. Zériahi, Approximation polynomiale et extension holomorphe avec crois-sance sur une variété algébrigue, Ann. Polon. Math., 63 (1996) 35-50.
• [10] A. Zériahi, Pluricomplex Green functions and approximation of holomorphic functions, in: Complex analysis, harmonic analysis and applications, Pitman Res. Notes Math. Ser. 347, Bordeaux 1995, 104-142.
• [11] A. Zériahi, A criterion of algebraicity for Lelong classes and analytic sets, preprint, Toulouse 1997.