量子图II：量子图和组合图的一些谱性质
Quantum Graphs II: Some spectral properties of quantum and combinatorial graphs
摘要：
本文研究了量子图和组合图的一些谱性质。量子图由于其在介观物理、纳米技术、光学等领域的广泛应用，近年来得到了广泛的研究。一个Schnol型定理证明，允许一个检测到一个点属于频谱时，广义本征函数与次指数增长积分估计是可用的。建立了一个关于"装饰“量子图的谱隙开放的定理（它的类似物是已知的组合情况）。它还表明，如果一个周期性的组合或量子图有一个点谱，它是由compounds支持的本征函数（“疤痕”）。
英文摘要：
The paper deals with some spectral properties of (mostly infinite) quantum and combinatorial graphs. Quantum graphs have been intensively studied lately due to their numerous applications to mesoscopic physics, nanotechnology, optics, and other areas. A Schnol type theorem is proven that allows one to detect that a point belongs to the spectrum when a generalized eigenfunction with an subexponential growth integral estimate is available. A theorem on spectral gap opening for ``decorated'' quantum graphs is established (its analog is known for the combinatorial case). It is also shown that if a periodic combinatorial or quantum graph has a point spectrum, it is generated by compactly supported eigenfunctions (``scars'').
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