Journal of the Mathematical Society of Japan

Removable singularities of holomorphic solutions of linear partial differential equations

Katsuju IGARI

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Abstract

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.

Article information

Source
J. Math. Soc. Japan, Volume 56, Number 1 (2004), 87-113.

Dates
First available in Project Euclid: 3 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1191418697

Digital Object Identifier
doi:10.2969/jmsj/1191418697

Mathematical Reviews number (MathSciNet)
MR2023455

Zentralblatt MATH identifier
1062.35009

Subjects
Primary: 35A20: Analytic methods, singularities
Secondary: 35A10: Cauchy-Kovalevskaya theorems 35A21: Propagation of singularities

Keywords
Removable singularities singular solutions propagation of singularities Cauchy-Kovalevskaya type theorem

Citation

IGARI, Katsuju. Removable singularities of holomorphic solutions of linear partial differential equations. J. Math. Soc. Japan 56 (2004), no. 1, 87--113. doi:10.2969/jmsj/1191418697. https://projecteuclid.org/euclid.jmsj/1191418697


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