Funcţii complexe de mai multe variabile |
trul |
||||
Cadre didactice indrumatoare |
Prof. Dr. KOHR Gabriela, gkohrmath.ubbcluj.ro |
Obiective |
Cursul isi propune introducerea si aprofundarea unor rezultate fundamentale din domeniul functiilor olomorfe de mai multe variabile complexe. |
Continut |
1. Functii olomorfe de mai multe variabile complexe. Proprietati generale. Definitii echivalente, formula de reprezentare integrala in polidisc, dezvoltare in serie de puteri. Teorema identitatii functiilor olomorfe, principiul maximului modulului, familii de functii olomorfe. Teorema lui Hartogs.
2. Aplicatii olomorfe. Proprietati generale. Aplicatii biolomorfe. Echivalenta dintre univalenta si biolomorfie. Teoremele lui Cartan de unicitate. Aplicatii la determinarea automorfismelor biolomorfe ale bilei unitate si polidiscului unitate. 3. Functii pluriarmonice si plurisubarmonice. Proprietati generale. 4. Domenii de olomorifie. Prorietati. Aplicatii si exemple. Convexitate olomorfa. Proprietati. Echivalenta dintre convexitatea olomorfa si domeniu de olomorfie. 5. Domenii pseudoconvexe. Pseudoconvexitate in sens Hartogs and Levi. Proprietati generale. 6. Subclase de aplicatii biolomorfe in bila unitate din C^n: aplicatii stelate si convexe. Teoreme de deformare, acoperire si distorsiune. Exemple. |
Bibliografie |
1. KOHR, GABRIELA: Basic Topics in Holomorphic Functions of Several Complex Variables. Cluj-Napoca: Cluj University Press, 2003.
2. GRAHAM, IAN - KOHR, GABRIELA: Geometric Function Theory in One and Higher Dimensions. New York: Marcel Dekker Inc, 2003. 3. CHABAT, BORIS V: Introduction a l'Analyse Complexe. Vol.II. Moscou: Ed. MIR, 1990. 4. GUNNING, ROBERT C: Introduction to Holomorphic Functions of Several Variables. vol.I. Monterey: Wadsworth & Brooks/Cole, 1990. 5. HORMANDER, LARS: An Introduction to Complex Analysis in Several Variables. Second Edition. Amsterdam-London: North-Holland Publ. Co., 1973. 6. KAUP, LUDGER - KAUP, BURCHARD: Holomorphic Functions of Several Variables. Berlin-New York: Walter de Gruyter & Co., 1983. 7. KRANTZ, STEVEN G: Function Theory of Several Complex Variables. Reprint of the 1992 Edition. Rhode Island: AMS Chelsea Publishing, Providence, 2001. 8. NARASIMHAN, RAGHAVAN: Several Complex Variables. Chicago: The University of Chicago Press, 1971. 9. RANGE, MICHAEL: Holomorphic Functions and Integral Representations in Several Complex Variables. New York: Springer-Verlag, 1986. 10. RUDIN, WALTER: Function Theory in the Unit Ball of C^n. New York: Springer-Verlag, 1980. |
Evaluare |
Examen (70%)+ activitate de seminar (30%). |
Legaturi: | Syllabus-urile tuturor disciplinelor Versiunea in limba engleza a acestei discipline Versiunea in format rtf a acestei discipline |