Symmetrizers for hyperbolic operators are obtained by diagonalizing the Bézoutian matrix of the principal symbols and its derivatives. Such diagonal symmetrizers are applied to the Cauchy problem for hyperbolic operators with triple characteristics. In particular, the Ivrii’s conjecture concerned with strongly hyperbolic operators with triple effectively hyperbolic characteristics is proved for differential operators with time dependent coefficients, also for third order differential operators with two independent variables with analytic coefficients.

中文翻译：

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具有三重特征的双曲算子的对角对称器

通过将主符号及其派生词的Bézoutian矩阵对角化，可以获得双曲算符的对称子。这种对角对称器被应用于具有三重特征的双曲算子的柯西问题。特别地，对于具有时间相关系数的微分算子，对于具有两个具有解析系数的自变量的三阶微分算子，证明了具有三重有效双曲特征的强双曲算子的Ivrii猜想。