English

Generalization of proximate order and applications

Complex Variables 2020-07-17 v1

Abstract

We introduce a concept of a quasi proximate order which is a generalization of a proximate order and allows us to study efficiently analytic functions whose order and lower order of growth are different. We prove an existence theorem of a quasi proximate order, i.e. a counterpart of Valiron's theorem for a proximate order. As applications, we generalize and complement some results of M. Cartwright and C.~N.~Lin\-den on asymptotic behavior of analytic functions in the unit disc.

Keywords

Cite

@article{arxiv.2007.08346,
  title  = {Generalization of proximate order and applications},
  author = {Igor Chyzhykov and Petro Filevych and Jouni Rättyä},
  journal= {arXiv preprint arXiv:2007.08346},
  year   = {2020}
}

Comments

18 pages

R2 v1 2026-06-23T17:10:07.452Z