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28.—Growth of Solutions of Algebraic Equations with Coefficients in a Group

Published online by Cambridge University Press:  14 February 2012

V. Marić  and
A. Sangalli
V. Marić
Affiliation:
University of Novi Sad, Yugoslavia and Istituto Matematico ‘Ulisse Dini’, Università di Firenze
A. Sangalli
Affiliation:
Istituto Matematico ‘Ulisse Dini’, Università di Firenze.
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Extract

1. In this paper we study the asymptotic behaviour of solutions of algebraic equations with real functions as coefficients, using mainly algebraic properties of the class to which the coefficients belong. To that end we introduce the notion of an m-group of functions and prove the main theorem by a procedure originated in [1]. As a corollary we obtain sufficient conditions for a class F of functions to possess the property that solutions of algebraic equations with coefficients in F are again members of F. We conclude by applying these results to the classical Hardy's logarithmico-exponential class ℋ [2]

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 72 , Issue 4 , 1975 , pp. 327 - 330
Copyright
Copyright © Royal Society of Edinburgh 1975

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References

References to Literature

[1] Marić, V., 1972. Asymptotic behavior of solutions of a nonlinear differential equation of the first order. J. Math. Analysis Applic., 38, 187–192.Google Scholar
[2] Hardy, G. H., 1954. Orders of Infinity. C.U.P.Google Scholar
[3] Robinson, A., 1972. On the real closure of a Hardy Field. In Theory of Sets and Topology (Eds. G., Asser, J., Flachmeyer and W., Rinow). Berlin: VEB Deutscher Verlag Wissen.Google Scholar
[4] Bourbaki, N., 1951. Fonctions d'une Variable Réelle, Ch. IV–VII. Paris: Hermann.Google Scholar