星形网络上多重隧道效应的Klein-Gordon方程：广义本征函数的展开
The Klein-Gordon equation with multiple tunnel effect on a star-shaped network: Expansions in generalized eigenfunctions
摘要：
我们考虑由n个半轴在原点连接而成的星形网络上的Klein-Gordon方程。我们加上一个势，它是常数，但在每个分支上不同。相应的空间算子是自伴的，我们国家明确表示其预解式和其决议的身份广义本征函数。这导致广义傅立叶型反演公式的广义本征函数的展开。该问题的特点是星形区域的非流形特征。因此，通过Sturm-Liouville系统理论的方法是不适合的。
英文摘要：
We consider the Klein-Gordon equation on a star-shaped network composed of n half-axes connected at their origins. We add a potential which is constant but different on each branch. The corresponding spatial operator is self-adjoint and we state explicit expressions for its resolvent and its resolution of the identity in terms of generalized eigenfunctions. This leads to a generalized Fourier type inversion formula in terms of an expansion in generalized eigenfunctions. The characteristics of the problem are marked by the non-manifold character of the star-shaped domain. Therefore the approach via the Sturm-Liouville theory for systems is not well-suited.
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。
