非对称Ornstein-Uhlenbeck算子的二次量子化和L^p-谱
Second quantization and the L^p-spectrum of nonsymmetric Ornstein-Uhlenbeck operators
摘要：
的频谱的第二个量子化和对称的第二个量子化的严格的希尔伯特空间收缩的计算明确和一致。作为应用，我们计算了与无限维Langevin方程$$ dU(t) = AU(t)dt + dW(t), $$相关的非对称Ornstein-Uhlenbeck算子$L$的谱，其中$A$是Banach空间$E$上强连续半群的生成元，$W$是$E$中的圆柱Wiener过程.在有限维空间$E$的情况下，我们恢复最近Metafune Pallara Priola公式的频谱$L$。
英文摘要：
The spectra of the second quantization and the symmetric second quantization of a strict Hilbert space contraction are computed explicitly and shown to coincide. As an application, we compute the spectrum of the nonsymmetric Ornstein-Uhlenbeck operator $L$ associated with the infinite-dimensional Langevin equation $$ dU(t) = AU(t)dt + dW(t), $$ where $A$ is the generator of a strongly continuous semigroup on a Banach space $E$ and $W$ is a cylindrical Wiener process in $E$. In the case of a finite-dimensional space $E$ we recover the recent Metafune-Pallara-Priola formula for the spectrum of $L$.
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