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polynomial regular function

Proceedings of the Edinburgh Mathematical Society (1)

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On α-Polynomial Regular Functions, with Applications to Ordinary Differential Equations
Peter Fenton, Janne Grohn, Janne Heittokangas, John Rossi, Jouni Rattya
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Proceedings of the Edinburgh Mathematical Society / Volume 57 / Issue 2 / June 2014

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13 March 2014, pp. 405-421
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This research deals with properties of polynomial regular functions, which were introduced in a recent study concerning Wiman-Valiron theory in the unit disc. The relation of polynomial regular functions to a number of function classes is investigated. Of particular interest is the connection to the growth class Gα, which is closely associated with the theory of linear differential equations with analytic coefficients in the unit disc. If the coefficients are polynomial regular functions, then it turns out that a finite set of real numbers containing all possible maximum modulus orders of solutions can be found. This is in contrast to what is known about the case when the coefficients belong to Gα.