论文标题
离散拉瓜操作员的热核
Heat kernels of the discrete Laguerre operators
论文作者
论文摘要
对于离散的laguerre操作员，我们通过借助雅各比多项式来表达相应的热核来明确计算相应的热核。这使我们能够证明热半群具有超取消性并计算相应的规范。一方面，这有助于我们回答有关马尔可夫半群的基本问题（复发，随机完整性）。另一方面，我们证明了Cwiekel-lieb-Rosenblum的类似物和Bargmann估计Laguerre操作员的扰动以及最佳的Hardy不平等。
For the discrete Laguerre operators we compute explicitly the corresponding heat kernels by expressing them with the help of Jacobi polynomials. This enables us to show that the heat semigroup is ultracontractive and to compute the corresponding norms. On the one hand, this helps us to answer basic questions (recurrence, stochastic completeness) regarding the associated Markovian semigroup. On the other hand, we prove the analogs of the Cwiekel-Lieb-Rosenblum and the Bargmann estimates for perturbations of the Laguerre operators, as well as the optimal Hardy inequality.
