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arXiv · 1103.2073

The Yosida Class is Universal

Norbert Steinmetz
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Abstract

We discuss families of meromorphic functions $f_h$ obtained from single functions $f$ by the re-scaling process $f_h(z)=h^{-α}f(h+h^{-β}z)$ generalising Yosida's process $f_h(z)=f(h+z)$. The main objective is to obtain information on the value distribution of the generating functions $f$ themselves. Among the most prominent generalised Yosida functions are first, second and fourth Painlevé transcendents. The Yosida class contains all limit functions of generalised Yosida functions--the Yosida class is universal.

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Norbert Steinmetz. 2011-03-10. The Yosida Class is Universal. https://arxiv.org/abs/1103.2073

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