Functions of finite type in several complex variables
Author:
Robert O. Kujala
Journal:
Trans. Amer. Math. Soc. 161 (1971), 327358
MSC:
Primary 32.12
MathSciNet review:
0281943
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Abstract: If is continuous and increasing then a meromorphic function f on is said to be of finite type if there are positive constants s, A, B and R such that for all where is the characteristic of f. It is shown that if is bounded for r sufficiently large and , then every meromorphic function of finite type is the quotient of two entire functions of finite type. This theorem is the result of a careful and detailed analysis of the relation between the growth of a function and the growth of its divisors. The central fact developed in this connection is: A nonnegative divisor on with is the divisor of an entire function of finite type if and only if there are positive constants A, B and R such that for all , all unit vectors in , and all natural numbers p. Here represents the lifting of the divisor to the plane via the map and is the valence function of that divisor. Analogous facts for functions of zero type are also presented.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197102819435
PII:
S 00029947(1971)02819435
Keywords:
Several complex variables,
meromorphic function,
holomorphic function,
characteristic of a meromorphic function,
valuedistribution theory,
divisors of a function,
plurisubharmonic functions,
Fourier coefficients of a meromorphic function,
growth functions,
growth indices,
finite type,
order and type of a meromorphic function
Article copyright:
© Copyright 1971
American Mathematical Society
