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January, 2004 Removable singularities of holomorphic solutions of linear partial differential equations
Katsuju IGARI
J. Math. Soc. Japan 56(1): 87-113 (January, 2004). DOI: 10.2969/jmsj/1191418697


In a complex domain VCn, let P be a linear holomorphic partial differential operator and K be its characteristic hypersurface. When the localization of P at K is a Fuchsian operator having a non-negative integral characteristic index, it is proved, under some conditions, that every holomorphic solution to Pu=0 in VK has a holomorphic extension in V. Besides, it is applied to the propagation of singularities for equations with non-involutive double characteristics.


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Katsuju IGARI. "Removable singularities of holomorphic solutions of linear partial differential equations." J. Math. Soc. Japan 56 (1) 87 - 113, January, 2004.


Published: January, 2004
First available in Project Euclid: 3 October 2007

zbMATH: 1062.35009
MathSciNet: MR2023455
Digital Object Identifier: 10.2969/jmsj/1191418697

Primary: 35A20
Secondary: 35A10 , 35A21

Keywords: Cauchy-Kovalevskaya type theorem , propagation of singularities , Removable singularities , Singular solutions

Rights: Copyright © 2004 Mathematical Society of Japan


Vol.56 • No. 1 • January, 2004
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