Several Complex Variables
ααααΌ 2012 Β· Springer Science & Business Media
ααααα
βα’αα‘α·α
ααααΌαα·α
208
ααααα
α’αααΈααααα βα’αα‘α·α ααααΌαα·αααα
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.
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...
αααααααβα αααΎαααα
ααΆααααααααααα βα’αα‘α·α ααααΌαα·αααα
ααααΆααααΎαα’αααΈααΆααααααΎαααααα’αααα
α’αΆαβααααααΆα
ααΌαααααααααΆααα αα·αβααααααα
ααα‘αΎααααααα·ααΈ Google Play Books αααααΆαα Android αα·α iPad/iPhone α ααΆβααααΎααααΆαααααβαααααααααααααααα·ααΆαα½αβααααΈβααααα’αααβ αα·αβα’αα»ααααΆαα±ααβα’αααα’αΆααααβααΆαα’ααΈαααΊαα·α α¬ααααΆαβα’ααΈαααΊαα·αβαα
αααααααΈααααααα
αα»αααααΌαααβαα½ααα αα·ααα»αααααΌααα
α’αααα’αΆα
ααααΆααααααα
ααΆααα‘αααααααΆααα·ααα
αααα»α Google Play αααααααΎαααααα·ααΈαα»αααααΆαα’ααΈαααΊαα·ααααα»ααα»αααααΌαααααααα’αααα
eReaders αα·αβα§αααααβαααααβααα
ααΎααααΈα’αΆααα
ααΎβα§ααααα e-ink ααΌα
ααΆβα§αααααα’αΆαβααααα
α’αα‘α·α
ααααΌαα·α Kobo α’αααααΉαααααΌαβααΆαααβα―αααΆα α αΎαβαααααααΆαα
βα§αααααβααααα’αααα ααΌαα’αα»ααααααΆαβααΆαααααΆααααα’α·αααααααααααααααααα½α ααΎααααΈαααααα―αααΆαβαα
α§αααααα’αΆαααααα
βα’αα‘α·α
ααααΌαα·ααααααααΆααα
