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The Yosida class is universal

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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 about the value distribution of the generating functions f themselves. Among the most prominent (generalised) Yosida functions are the elliptic functions and also some first, second and fourth Painlevé transcendents. The Yosida class A 0 contains all limit functions of generalised Yosida functions-the Yosida class is universal.

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  1. Fakultät für Mathematik, Technische Universität Dortmund, D-44221, Dortmund, Germany

    Norbert Steinmetz

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  1. Norbert Steinmetz
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Correspondence to Norbert Steinmetz.

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Steinmetz, N. The Yosida class is universal. JAMA 117, 347–364 (2012). https://doi.org/10.1007/s11854-012-0025-3

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  • DOI: https://doi.org/10.1007/s11854-012-0025-3

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