Half-line Schrödinger operators with no bound states
Half-line Schrödinger operators with no bound states
复制标题
无束缚态的半线薛定谔算子
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
R. Killip
中科院分区：
文献类型：
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作者：
D. Damanik;R. Killip
为了方便起见，我们要求位势V是一致局部平方可积的。我们把这类函数的Banach空间记为l~（L2）.自由算子，也就是说，当V-0时，可以通过傅里叶变换对角化。这表明它们分别具有谱[-2，2]和[0，ω），并且在这两种情况下，谱是纯绝对连续的。对于一般的离散算子，仅仅是谱包含在[-2，2]中的事实就迫使它是纯绝对连续的。这是我们的第一个主要结果：
acting in L2([0, c~)) with the boundary condition r For convenience, we require that the potential, V, be uniformly locally square integrable. We write l~(L 2) for the Banach space of such functions. The free operators, that is, when V--0, can be diagonalized by the Fourier transform. This shows that they have spectra [-2, 2] and [0, co), respectively, and that in both cases, the spectrum is purely absolutely continuous. For a general discrete operator, the mere fact that the spectrum is contained in [-2, 2] forces it to be purely absolutely continuous. This is our first main result: