Spectral and scattering theory for Schrödinger operators
Spectral and scattering theory for Schrödinger operators
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薛定谔算子的光谱和散射理论
DOI：
10.1007/bf00252679
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发表时间：
1969
影响因子：
2.5
通讯作者：
G. Schmidt
中科院分区：
文献类型：
--
作者：
Preben K. Alsholm;G. Schmidt
本文讨论了薛定谔算子A+ V的谱和散射理论的推广、统一和简化，其中A是拉普拉斯算子，V是合适的势函数。我们在POVZNER [14]， IKEBE[6]和THOE[21]描述的框架内工作，但将其扩展到包括[11]和[12]中描述的KURODA的结果。设A表示自伴随算子-A，定义在L2= L2 (Rn)*(n> 3)中，定域D (A)= h2（具有2阶平方可积导数的平方可积函数的Sobolev空间）。利用傅里叶变换~-:L2 （R~）—* L2 （R~）完整地描述了该算子的谱理论，定义为n_ o-~-f (~)= lim (27r) 2s c~（x， R）
This paper is concerned with the generalization, unification, and simplification of the spectral and scattering theory of the Schrfdinger operator-A+ V, where A is the Laplacian and V is an appropriate potential function. We work within the framework described by POVZNER [14], IKEBE [6], and THOE [21], but extend this to include also the results of KURODA described in [11] and [12]. Let A denote the self-adjoint operator-A defined in L2= L2 (Rn)*(n> 3) with domain D (A)= H 2 (the Sobolev space of square integrable functions having square integrable derivatives up to order 2). The spectral theory of this operator is described completely with the help of the Fourier transform~-: L2 (R~)--* L 2 (R~) defined by n_ o-~-f (~)= lim (27r) 2 S c~(x, r