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Newton polygons and gevrey indices for linear partial differential operators

Published online by Cambridge University Press:  22 January 2016

Masatake Miyake
Affiliation:
Department of Mathematics, College of General Education, Nagoya University, Nagoya 464-01, Japan
Yoshiaki Hashimoto
Affiliation:
Department of Mathematics, College of General Education, Nagoya City University, Nagoya 467, Japan
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This paper is a continuation of Miyake [7] by the first named author. We shall study the unique solvability of an integro-differential equation in the category of formal or convergent power series with Gevrey estimate for the coefficients, and our results give some analogue in partial differential equations to Ramis [10, 11] in ordinary differential equations.

In the study of analytic ordinary differential equations, the notion of irregularity was first introduced by Malgrange [3] as a difference of indices of a differential operator in the categories of formal power series and convergent power series. After that, Ramis extended his theory to the category of formal or convergent power series with Gevrey estimate for the coefficients. In these studies, Ramis revealed a significant meaning of a Newton polygon associated with a differential operator.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1992

References

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[13] Yonemura, A., Newton polygons and formal Gevrey classes, Publ. Res. Inst. Math. Sci., 26 (1990), 197204.CrossRefGoogle Scholar
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