Variations on the proximate order
Complex Variables
2019-12-03 v1
Abstract
The concept of proximate order is widely used in the theories of entire, meromorphic, subharmonic and plurisubharmonic functions. We give a general interpretation of this concept as a proximate growth function relative to a model growth function. If a function is the proximate growth function with respect to the identity function on the positive semi-axis, then the logarithm of this function is the classical proximate order. Our definition uses only one condition. This form of definition is also new for the classical proximate order.
Cite
@article{arxiv.1912.00746,
title = {Variations on the proximate order},
author = {Bulat N. Khabibullin},
journal= {arXiv preprint arXiv:1912.00746},
year = {2019}
}
Comments
5 pages, in Russian