Abstract

We consider a general scalar self-adjoint elliptic second order operator with general boundary conditions on an arbitrary metric graph containing a subgraph with edges of lengths proportional to a small parameter. We show that the resolvent of such operator is holomorphic in the small parameter and provide its representations by Taylor series. The coefficients of the series are found rather explicitly.

中文翻译：

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具有小边的量子图：溶剂的全纯

摘要

我们在任意度量图上考虑具有一般边界条件的一般标量自伴随椭圆二阶算子，该图包含长度与小参数成正比的子图。我们证明了这种算子的解析在小参数中是全纯的，并通过泰勒级数提供了它的表示。相当明确地找到了该系列的系数。