Linearly invariant families of holomorphic mapping in Cn. Transition to other dimensions

• Autorzy: Liczberski P.
• Języki publikacji: EN

Abstrakty

EN

In the paper there are given new applications of dimension reduction method (from [3]) of studing linearly invariant families of holomorphic mappings in Cn. There also included generalizing modifications of this method.

Słowa kluczowe

EN

locally biholomorphic mappings; linearly invariant families

PL

liniowo niezmienne rodziny

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2003
• Tom: Vol. 9, nr 2
• Strony: 237--248
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Liczberski P.

• Institute of Mathematics Technical University of Łódź Żwirki 36 90-924 Łódź, Poland,

Bibliografia

• [1] Barnard, R. W., FitzGerald, С. H., Gong, S., Distortion theorem for biholomorphic mappings in Cn, Trans. Amer. Math. Soc. 344 (1994), 907-924.
• [2] Godula, J., Liczberski, P., Starkov, V. V., Order of linearly invariant family of mappings in Cn, Complex Variables Theory Appl. 42 (2000), 89-96.
• [3] Liczberski, P., Starkov, V. V., Linearly invariant families of holomorphic mappings of a ball. The dimension reduction method, Siberian Math. J. 42 (2001), 715-730. Translated from Sibirsk. Mat. Zh. 42 (2001), 849-867.
• [4] Liczberski, P., Starkov, V. V., Regularity theorems for linearly invariant families of mappings in Cn, Ann. Univ. Mariae Curie-Sklodowska Sect. A 54 (2000), 61-73.
• [5] Liczberski, P., Starkov, V. V., Linearly invariant families of holomorphic mappings of a ball. Transition to higher dimensions (in Russian), Tr. Petrozavodsk. Gos. Univ. Ser. Mat. 10 (2003), (to appear).
• [6] Pfaltzgraff, J. A., Distortion of locally biholomorphic maps of the N-ball, Complex Variables Theory Appl. 33 (1997), 239-253.
• [7] Pfaltzgraff, J. A., Erratum “Distortion of locally biholomorphic maps of the N- ball”, Complex Variables Theory Appl. 45 (2001), 197-200.
• [8] Pfaltzgraff, J. A., Suffridge, T. J., An extension theorem and linear invariant families generated by starlike maps, Ann. Univ. Mariae Curie-Sklodowska Sect. A 53 (1999), 193-207.
• [9] Pommerenke, Ch., Linear-invariante Familien analytischen Funktionen I, Math. Ann. 155 (1964), 108-154.
• [10] Roper, K. A., Suffridge, T. J., Convex mappinqs on the unit ball of Cn, J. Anal. Math. 65 (1995), 333-347.
• [11] Rudin, W., Function theory in the unit ball of Cn, Springer Verlag, Berlin- Heidelberg-New York, 1980.