Holomorphic Functions of Finite Order in Several Complex Variables, Issues 21-25In this expository paper one fundamental aspect of the theory, the construction of holomorphic functions with growth estimates to given zero sets was selected as the central topic of the survey. In addition to two main theorems of value distribution are stated for a meromorphic map of a hermitian vector space into a complex projective space because of the fundamental importance of these theorems. |
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abelian divisor algebraic analytic set analytic subset Assume that ƒ Blaschke condition canonical function chain of dimension class C¹ Define A supp diffeomorphism entire function exponent of convergence f is holomorphic finite order Fourier series function h function of class function on W(R functions of finite Hence hermitian vector space holomorphic function holomorphic map homogeneous polynomial implies increasing function integrals exist Jensen-Poisson formula Jensen's formula Kaehler manifold Kujala 23 LEMMA Let f Let G Let h Let q Let v0 log f(0 log h(3 m²(r Main Theorem Math meromorphic function meromorphic map minimal type Moreover N₁(r Ng(r nonnegative divisor open subset Ord f P₁ pluri-subharmonic function polydisc polynomial of degree PROOF Proposition 3.9 RONKIN 35 S₁ satisfies a Blaschke subset of Cm Sw(r Take Į ER+m theta function weight function weight q