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数学与物理
应用数学进展
Vol. 11 No. 10 (October 2022)
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完备次黎曼流形上Schrödinger算子的自伴性
The Self-Adjiontness of the Schrödinger Operator on Complete Sub-Riemannian Manifolds
DOI:
10.12677/AAM.2022.1110764
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被引量
下载: 334
浏览: 416
作者:
陶一涞
:浙江师范大学,数学与计算机科学学院,浙江 金华
关键词:
次黎曼流形
;
SchrO
¨
dinger算子
;
下有界
;
本质自伴
;
Sub-Riemannian Manifold
;
SchrO
¨
dinger Operator
;
Semibounded
;
Essentially Self-Adjoint
摘要:
本文研究次黎曼流形上的Schrödinger算子在无界区域内的性质,并得到在完备的次黎曼流形上下有界的该算子必定是本质自伴的。
Abstract:
This paper studies the properties of the Schrödinger operator on sub-Riemannian manifolds in the unbounded domain. It is further studied that the semibounded operator must be essentially self-adjoint on complete sub-Riemannian manifolds.
文章引用:
陶一涞. 完备次黎曼流形上Schrödinger算子的自伴性[J]. 应用数学进展, 2022, 11(10): 7201-7208.
https://doi.org/10.12677/AAM.2022.1110764
参考文献
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https://doi.org/10.1007/s12220-020-00408-z
[8]
邹文婷. 次黎曼流形上的次椭圆调和映射梯度估计[J]. 应用数学进展, 2021, 10(11): 3912-3922.
https://doi.org/10.12677/AAM.2021.1011416
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