Abstract We describe the spectrum of degenerate hypoelliptic Ornstein-Uhlenbeck operators A = ∑ i , j = 1 n q i j D i j + ∑ i , j = 1 n b i j x j D i in L p ( R n ) , 1 ≤ p + ∞ , and in C 0 ( R n ) . We show that the spectrum of A is the sum of ( − ∞ , 0 ] and the spectrum of the drift term. Our result gives a complete picture of the spectral properties of Ornstein-Uhlenbeck operators in L p spaces.

中文翻译：

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退化亚椭圆 Ornstein-Uhlenbeck 算子的 L 谱

摘要 我们描述了退化亚椭圆 Ornstein-Uhlenbeck 算子的频谱 A = ∑ i , j = 1 nqij D ij + ∑ i , j = 1 nbijxj D i in L p ( R n ) , 1 ≤ p + ∞ , and in C 0 (Rn)。我们证明 A 的谱是 ( − ∞ , 0 ] 和漂移项的谱之和。我们的结果给出了 L p 空间中 Ornstein-Uhlenbeck 算子的谱性质的完整图片。