...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Infinite dimensional analysis, quantum probability, and related topics >Second quantization and the L-P-spectrum of nonsymmetric Ornstein-Uhlenbeck operators
【24h】

Second quantization and the L-P-spectrum of nonsymmetric Ornstein-Uhlenbeck operators

机译：非对称Ornstein-Uhlenbeck算子的二次量化和L-P谱

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

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. Assuming the existence of an invariant measure mu for L, under suitable assumptions on A we show that the spectrum of L in the space L-p (E, mu) (1 < p < infinity) is given by sigma(L) = {Sigma(j+1)(n) k(j)z(j) : k(j) is an element of N, z(j) is an element of sigma(A(mu)); j = 1,...,n;n >= 1} where A(mu) is the generator of a Hilbert space contraction semigroup canonically associated with A and mu. We prove that the assumptions on A are always satisfied in the strong Feller case and in the finite-dimensional case. In the latter case we recover the recent Metafune-Pallara-Priola formula for sigma(L).
机译：严格计算希尔伯特空间收缩的第二量化和对称第二量化的频谱，并显示它们是一致的。作为应用，我们计算与无限维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是强连续半群的生成器在Banach空间E上，W是E中的一个圆柱维纳过程。假设L存在不变度量mu，在A的适当假设下，我们证明L在空间Lp（E，mu）（1 < p <无穷大）由sigma（L）= {Sigma（j + 1）（n）k（j）z（j）给出：k（j）是N的元素，z（j）是sigma的元素（A（μ））; j = 1，...，n; n> = 1}其中A（mu）是与A和mu正则相关的希尔伯特空间收缩半群的生成器。我们证明，在强Feller情况和有限维情况下，始终满足A的假设。在后一种情况下，我们恢复了最近的Sigma（L）的Metafune-Pallara-Priola公式。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号