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On α-Polynomial Regular Functions, with Applications to Ordinary Differential Equations

Published online by Cambridge University Press:  13 March 2014

Peter Fenton ,
Janne Grohn ,
Janne Heittokangas ,
John Rossi  and
Jouni Rattya
Peter Fenton
Affiliation:
Department of Mathematics and Statistics, University of Otago, PO Box 56, Dunedin 9054, New Zealand, ([email protected])
Janne Grohn
Affiliation:
Department of Physics and Mathematics, University of Eastern Finland, PO Box 111, FI-80101 Joensuu, Finland, ([email protected]; [email protected]; [email protected])
Janne Heittokangas
Affiliation:
Department of Physics and Mathematics, University of Eastern Finland, PO Box 111, FI-80101 Joensuu, Finland, ([email protected]; [email protected]; [email protected])
John Rossi
Affiliation:
Department of Mathematics, Virginia Tech, 460 McBryde, Blacksburg, VA 24061-0123, USA, ([email protected])
Jouni Rattya
Affiliation:
Department of Physics and Mathematics, University of Eastern Finland, PO Box 111, FI-80101 Joensuu, Finland, ([email protected]; [email protected]; [email protected])
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Abstract

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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.

Keywords

annular functiongrowth of solutionslinear differential equationpolynomial regular functionPrimary 30D3530D40Secondary 30E1534M10
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 57 , Issue 2 , June 2014 , pp. 405 - 421
Copyright
Copyright © Edinburgh Mathematical Society 2014 

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