Approximation by Proper Holomorphic Maps and Tropical Power Series

作者：Abakumov Evgeny; Doubtsov Evgueni^*

来源：Constructive Approximation, 2018, 47(2): 321-338.

DOI：10.1007/s00365-017-9375-5

• Entire function
• Radial weight
• Proper holomorphic map
• Tropical power series
• Essential weight
• Log-convex function

Let be an unbounded radial weight on the complex plane. We study the following approximation problem: find a proper holomorphic map such that |f| is equivalent to . We give several characterizations of those for which the problem is solvable. In particular, a constructive characterization is given in terms of tropical power series. Moreover, the following natural objects and properties are involved: essential weights on the complex plane, approximation by power series with positive coefficients, and approximation by the maximum of a holomorphic function modulus. Extensions to several complex variables and approximation by harmonic maps are also considered.

• 出版日期2018-4