By H. Grauert, K. Fritzsche

ISBN-10: 1461298741

ISBN-13: 9781461298748

ISBN-10: 1461298768

ISBN-13: 9781461298762

The current booklet grew out of introductory lectures at the thought offunctions of numerous variables. Its motive is to make the reader regular, by means of the dialogue of examples and targeted situations, with an important branches and techniques of this thought, between them, e.g., the issues of holomorphic continuation, the algebraic therapy of energy sequence, sheaf and cohomology idea, and the genuine equipment which stem from elliptic partial differential equations. within the first bankruptcy we commence with the definition of holomorphic services of a number of variables, their illustration by way of the Cauchy imperative, and their strength sequence enlargement on Reinhardt domain names. It seems that, in l:ontrast ~ 2 there exist domain names G, G c en to the idea of a unmarried variable, for n with G c G and G "# G such that every functionality holomorphic in G has a continuation on G. domain names G for which this sort of G doesn't exist are known as domain names of holomorphy. In bankruptcy 2 we provide a number of characterizations of those domain names of holomorphy (theorem of Cartan-Thullen, Levi's problem). We eventually build the holomorphic hull H(G} for every area G, that's the biggest (not unavoidably schlicht) area over en into which every functionality holomorphic on G should be continued.