Abstract
We study the solvability of partial differential operators with multiple characteristics, whose characteristic varieties have singularities outside the zero-section of the cotangent bundle. By making use of the theory of bimicrolocalization, we prove the solvability for a class of operators in the space of Sato's hyperfunctions. This result generalizes the classical results due to Bony-Schapira and Kashiwara-Kawai etc. To obtain it, we also discuss the solvability for systems of partial differential equations.
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