Ground-state positivity, negativity, and compactness for a Schrödinger operator in RN
Ground-state positivity, negativity, and compactness for a Schrödinger operator in RN
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RN 中薛定谔算子的基态正性、负性和紧性
DOI：
10.1016/j.jfa.2006.12.007
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发表时间：
2007
影响因子：
1.7
通讯作者：
P. Takáč
中科院分区：
文献类型：
--
作者：
B. Alziary;J. Fleckinger;P. Takáč
我们处理L2（RN）上的薛定谔算子A=−Δ+q（x）·，其中势q：RN→[q 0，∞）在下面有界，并且满足关于无穷大增长的一些合理假设（比|X| 2AS| X| →∞）。我们主要关心的是作为Banach空间X上算子的A的预解式（A−λI）− 1的紧性，其中φ表示A的基态。如果Λ是A的基态能量，我们证明了限制算子（A−λI）−1：X→X对λ∈（−∞，Λ）不仅是有界的，而且是紧的.特别地，A在L2（RN）和X中的谱重合;每个本征函数都属于X。作为另一个结果，我们得到了一个最大值和一个反最大值原理。
We treat the Schrödinger operator A=−Δ+q(x)• on L2(RN) with the potential q:RN→[q0,∞) bounded below and satisfying some reasonable hypotheses on the growth at infinity (faster than |x|2as |x|→∞). We are concerned primarily with the compactness of the resolvent (A−λI)−1of A as an operator on the Banach space X, where φ denotes the ground state for A. If Λ is the ground state energy for A, we show that the restricted operator (A−λI)−1:X→X is not only bounded, but also compact for λ∈(−∞,Λ). In particular, the spectra of A in L2(RN) and X coincide; each eigenfunction belongs to X. As another consequence, we obtain a maximum and an anti-maximum principles.