论文标题
Burchnall-Chaundy理论
Burchnall-Chaundy Theory
论文作者
论文摘要
Burchnall-Chaundy理论涉及所有对通勤差异操作员的分类。我们用集成系统的光谱数据语言用这种理论来表达这一理论。 特别是，我们定义了等级1交换代数的光谱数据。我们解决了此类数据的逆问题，即，我们证明了代数$ a $（本质上）由其光谱数据唯一决定。 $ a $的异构类型由基础光谱曲线独特地确定。
The Burchnall-Chaundy theory concerns the classification of all pairs of commuting ordinary differential operators. We phrase this theory in the language of spectral data for integrable systems. In particular, we define spectral data for rank 1 commutative algebras $A$ of ordinary differential operators. We solve the inverse problem for such data, i.e. we prove that the algebra $A$ is (essentially) uniquely determined by its spectral data. The isomorphy type of $A$ is uniquely determined by the underlying spectral curve.
