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arXiv · 2007.08346

Generalization of proximate order and applications

Igor Chyzhykov·Petro Filevych·Jouni Rättyä
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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.

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Igor Chyzhykov, Petro Filevych, Jouni Rättyä. 2020-07-16. Generalization of proximate order and applications. https://arxiv.org/abs/2007.08346

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