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A canonical form of a system of microdifferential equations with non-involutory characteristics and branching of singularities

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Abstract

We study a system ℳ of microdifferential (=pseudodifferential) equations. We assume that the characteristic varietyV of ℳ takes the formV=V 1∪V2; hereV 1andV 2are regular involutory submanifolds and intersect normally, andV 1∩V2is non-involutory and 1-codimensional both inV 1and inV 2. We also assume that ℳ has regular singularities alongV. Then we give a canonical form of ℳ in the complex domain. This enables us to investigate the branching of supports of microfunction solutions of ℳ when ℳ is hyperbolic.

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  1. Department of Mathematics, Faculty of Science, University of Tokyo, Hongo, 113, Tokyo, Japan

    Toshinori Ôaku

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  1. Toshinori Ôaku
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Ôaku, T. A canonical form of a system of microdifferential equations with non-involutory characteristics and branching of singularities. Invent Math 65, 491–525 (1982). https://doi.org/10.1007/BF01396633

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  • DOI: https://doi.org/10.1007/BF01396633

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