Abstract:
In this work, the holomorphic functions with pre-defined conditions will be studied. We can start by studying numerical infinite products and infinite products of holomorphic functions. Above all results that will be presented will have to do with its use in the following chapters. Later, we will study analytical functions with pre-defined zeros, whose existence is assured by the Theorem of Weierstrass.The meromorphic functions with pre-defined main part will also be studied. In this case, the Theorem of Mittag-Leffer give us the way to define these functions. In the last chapter, we will see that under certain conditions related to the set of poles of a defined function by a series of Goursat and to the set of zeros of a holomorphic function, the maximal domain of existence of a holomorphic function is its domain of holomorphy.

Funções holomorfas em condições pré-definidas (pdf) »»