Several Complex Variables
12.2012β―Π³. Β· Graduate Texts in Mathematics ΠΠ½ΠΈΠ³Π° 38 Β· Springer Science & Business Media
ΠΠ»Π΅ΠΊΡΡΠΎΠ½Π½Π° ΠΊΠ½ΠΈΠ³Π°
208
Π‘ΡΡΠ°Π½ΠΈΡΠΈ
reportΠΡΠ΅Π½ΠΊΠΈΡΠ΅ ΠΈ ΠΎΡΠ·ΠΈΠ²ΠΈΡΠ΅ Π½Π΅ ΡΠ° ΠΏΠΎΡΠ²ΡΡΠ΄Π΅Π½ΠΈ Β ΠΠ°ΡΡΠ΅ΡΠ΅ ΠΏΠΎΠ²Π΅ΡΠ΅
ΠΡΠΈΡΠΊΠΎ Π·Π° ΡΠ°Π·ΠΈ Π΅Π»Π΅ΠΊΡΡΠΎΠ½Π½Π° ΠΊΠ½ΠΈΠ³Π°
The present book grew out of introductory lectures on the theory offunctions of several variables. Its intent is to make the reader familiar, by the discussion of examples and special cases, with the most important branches and methods of this theory, among them, e.g., the problems of holomorphic continuation, the algebraic treatment of power series, sheaf and cohomology theory, and the real methods which stem from elliptic partial differential equations. In the first chapter we begin with the definition of holomorphic functions of several variables, their representation by the Cauchy integral, and their power series expansion on Reinhardt domains. It turns out that, in l:ontrast ~ 2 there exist domains G, G c en to the theory of a single variable, for n with G c G and G "# G such that each function holomorphic in G has a continuation on G. Domains G for which such a G does not exist are called domains of holomorphy. In Chapter 2 we give several characterizations of these domains of holomorphy (theorem of Cartan-Thullen, Levi's problem). We finally construct the holomorphic hull H(G} for each domain G, that is the largest (not necessarily schlicht) domain over en into which each function holomorphic on G can be continued.
ΠΡΠ΅Π½Π΅ΡΠ΅ ΡΠ°Π·ΠΈ Π΅Π»Π΅ΠΊΡΡΠΎΠ½Π½Π° ΠΊΠ½ΠΈΠ³Π°
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ΠΠ°ΠΏΡΠΎΠΏΠΈ ΠΈ ΠΊΠΎΠΌΠΏΡΡΡΠΈ
ΠΠΎΠΆΠ΅ΡΠ΅ Π΄Π° ΡΠ»ΡΡΠ°ΡΠ΅ Π·Π°ΠΊΡΠΏΠ΅Π½ΠΈΡΠ΅ ΠΎΡ Google Play Π°ΡΠ΄ΠΈΠΎΠΊΠ½ΠΈΠ³ΠΈ ΠΏΠΎΡΡΠ΅Π΄ΡΡΠ²ΠΎΠΌ ΡΠ΅Π± Π±ΡΠ°ΡΠ·ΡΡΠ° Π½Π° ΠΊΠΎΠΌΠΏΡΡΡΡΠ° ΡΠΈ.
ΠΠ»Π΅ΠΊΡΡΠΎΠ½Π½ΠΈ ΡΠ΅ΡΡΠΈ ΠΈ Π΄ΡΡΠ³ΠΈ ΡΡΡΡΠΎΠΉΡΡΠ²Π°
ΠΠ° Π΄Π° ΡΠ΅ΡΠ΅ΡΠ΅ Π½Π° ΡΡΡΡΠΎΠΉΡΡΠ²Π° Ρ Π΅Π»Π΅ΠΊΡΡΠΎΠ½Π½ΠΎ ΠΌΠ°ΡΡΠΈΠ»ΠΎ, ΠΊΠ°ΡΠΎ Π½Π°ΠΏΡΠΈΠΌΠ΅Ρ Π΅Π»Π΅ΠΊΡΡΠΎΠ½Π½ΠΈΡΠ΅ ΡΠ΅ΡΡΠΈ ΠΎΡ Kobo, ΡΡΡΠ±Π²Π° Π΄Π° ΠΈΠ·ΡΠ΅Π³Π»ΠΈΡΠ΅ ΡΠ°ΠΉΠ» ΠΈ Π΄Π° Π³ΠΎ ΠΏΡΠ΅Ρ
Π²ΡΡΠ»ΠΈΡΠ΅ Π½Π° ΡΡΡΡΠΎΠΉΡΡΠ²ΠΎΡΠΎ ΡΠΈ. ΠΠ·ΠΏΡΠ»Π½Π΅ΡΠ΅ ΠΏΠΎΠ΄ΡΠΎΠ±Π½ΠΈΡΠ΅ ΠΈΠ½ΡΡΡΡΠΊΡΠΈΠΈ Π² ΠΠΎΠΌΠΎΡΠ½ΠΈΡ ΡΠ΅Π½ΡΡΡ, Π·Π° Π΄Π° ΠΏΡΠ΅Ρ
Π²ΡΡΠ»ΠΈΡΠ΅ ΡΠ°ΠΉΠ»ΠΎΠ²Π΅ΡΠ΅ Π² ΠΏΠΎΠ΄Π΄ΡΡΠΆΠ°Π½ΠΈΡΠ΅ Π΅Π»Π΅ΠΊΡΡΠΎΠ½Π½ΠΈ ΡΠ΅ΡΡΠΈ.
