## Journal of the Mathematical Society of Japan

### Removable singularities of holomorphic solutions of linear partial differential equations

Katsuju IGARI

#### Abstract

In a complex domain $V\subset C^{n}$, 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 $V\backslash K$ 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

https://projecteuclid.org/euclid.jmsj/1191418697

Digital Object Identifier
doi:10.2969/jmsj/1191418697

Mathematical Reviews number (MathSciNet)
MR2023455

Zentralblatt MATH identifier
1062.35009

#### 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