Heat Kernel Expansions on the Integers
Heat Kernel Expansions on the Integers
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整数上的热核展开
DOI：
10.1023/a:1016258207606
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
P. Iliev
中科院分区：
文献类型：
--
作者：
F. Grünbaum;P. Iliev
对于实线上的热方程ut=uxx+Vu，存在一些显著的势V，其基本解的渐近展开成为有限和，并给出了精确的公式。我们证明，当用整数代替实行时，也会出现类似的现象。在这种情况下二阶导数被二阶差分算子L0代替。如果L表示对L0进行有限次达布变换的结果，则ut=Lu的基本解由包含虚参贝塞尔函数I的有限项和给出。
In the case of the heat equation ut=uxx+Vu on the real line, there are some remarkable potentials V for which the asymptotic expansion of the fundamental solution becomes a finite sum and gives an exact formula.We show that a similar phenomenon holds when one replaces the real line by the integers. In this case the second derivative is replaced by the second difference operator L0. We show if L denotes the result of applying a finite number of Darboux transformations to L0 then the fundamental solution of ut=Lu is given by a finite sum of terms involving the Bessel function I of imaginary argument.