关于Urbanik半群与Mehler半群的关系
On Relations Between Urbanik and Mehler Semigroups
摘要：
证明了算子自分解测度，或者更精确地说是它们的Urbanik可分解半群，诱导出有界线性算子的广义Mehler半群.此外，这些半群可以表示为算子值函数关于随机Lévy过程的随机积分。我们的巴拿赫空间设置是在对比希尔伯特空间上的广义Mehler半群迄今为止和最经常的研究。此外，我们给出了随机积分表示的新的证明。
英文摘要：
It is shown that operator-selfdecomposable measures, or more precisely their Urbanik decomposability semigroups, induce generalized Mehler semigroups of bounded linear operators. Moreover, those semigroups can be represented as random integrals of operator valued functions with respect to stochastic Lévy processes. Our Banach space setting is in the contrast with the Hilbert spaces on which so far and most often the generalized Mehler semigroups were studied. Furthermore, we give new proofs of the random integral representation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
