The Yosida Class is Universal

Details The Yosida Class is Universal The Yosida Class is Universal

2011-03-10

arxiv.org/abs/1103.2073v1

Mathematics

Complex Variables

Scientific paper

We discuss families of meromorphic functions $f_h$ obtained from single functions $f$ by the re-scaling process $f_h(z)=h^{-\alpha}f(h+h^{-\beta}z)$ 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 Painlev\'e transcendents. The Yosida class contains all limit functions of generalised Yosida functions--the Yosida class is universal.

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