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Wiener-Hopf equation and Fredholm property of the Goursat problem in Gevrey space

Published online by Cambridge University Press:  22 January 2016

Masatake Miyake  and
Masafumi Yoshino
Masatake Miyake
Affiliation:
Department of Mathematics, School of Science, Nagoya University, Nagoya 464-01, Japan
Masafumi Yoshino
Affiliation:
Faculty of Economics, Chuo University, Higashinakano, Hachioji, Tokyo 192-03, Japan
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In the study of ordinary differential equations, Malgrange ([Ma]) and Ramis ([R1], [R2]) established index theorem in (formal) Gevrey spaces, and the notion of irregularity was nicely defined for the study of irregular points. In their studies, a Newton polygon has a great advantage to describe and understand the results in visual form. From this point of view, Miyake ([M2], [M3], [MH]) studied linear partial differential operators on (formal) Gevrey spaces and proved analogous results, and showed the validity of Newton polygon in the study of partial differential equations (see also [Yn]).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 135 , September 1994 , pp. 165 - 196
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1994

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