离散Laguerre算子的热核
Heat kernels of the discrete Laguerre operators
摘要：
对于离散的Laguerre算子，我们明确地计算相应的热核表示他们的帮助下，雅可比多项式。这使我们能够证明热半群是超压缩的，并计算相应的范数。一方面，这有助于我们回答关于相关马尔可夫半群的基本问题（递归性，随机完备性）。另一方面，我们证明了Laguerre算子扰动的Cwiekel-Lieb-Rosenblum估计和Bargmann估计的类似物，以及最优Hardy不等式。
英文摘要：
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.
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