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On the analyticity of the locus of singularity of real analytic solutions with minimal dimension

Published online by Cambridge University Press:  22 January 2016

Akira Kaneko
Akira Kaneko*
Affiliation:
Department of Mathematics, College of General Education, University of Tokyo, 3-8-1, Komaba, Meguro-ku Tokyo 153, Japan
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Let P(x, D) be a linear partial differential operator with real analytic coefficients and let C ⊂ Rn be a germ of closed subset, say at the origin. We say that C is (the locus of) an irremovable singularity of a real analytic solution u of P(x, D)u = 0 if u is defined outside C on a neighborhood Ω of 0 but cannot be extended to the whole neighborhood Ω even as a hyperfunction solution of P(x, D)u = 0. This usage of the word “singularity” is the same as the one for the analytic functions in complex analysis, and is different of the usual usage of “singularities of solutions” in the theory of partial differential equations.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 104 , December 1986 , pp. 63 - 84
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1986

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