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, PDF, HTML, 下载: 256  浏览: 328 
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

[1] Ikebe, T. and Kato, T. (1962) Uniqueness of the Self-Adjoint Extension of Singular Elliptic Differential Operators. Archive for Rational Mechanics and Analysis, 9, 77-92.
https://doi.org/10.1007/BF00253334
[2] Stummel, F. (1956) Singula¨re elliptische Differentialoperatoren in Hilbertschen R¨aumen. Math- ematische Annalen, 132, 150-176.
https://doi.org/10.1007/BF01452327
[3] Wienholtz, E. (1958) Halbbeschra¨nkte partielle Differentialoperatoren zweiter Ordnung vom elliptischen Typus. Mathematische Annalen, 135, 50-80.
https://doi.org/10.1007/BF01350827
[4] Strichartz, R.S. (1983) Analysis of the Laplacian on the Complete Riemannian Manifold. Journal of Functional Analysis, 52, 48-79.
https://doi.org/10.1016/0022-1236(83)90090-3
[5] Chernoff, P.R. (1973) Essential Self-Adjointness of Powers of Generators of Hyperbolic Equa- tions. Journal of Functional Analysis, 12, 401-414.
https://doi.org/10.1016/0022-1236(73)90003-7
[6] Pigola, S., Rigoli, M. and Setti, A.G. (2008) Vanishing and Finiteness Results in Geometric Analysis: A Generalization of the Bochner Technique. Springer Science & Business Media, Berlin.
[7] Dong, Y. (2021) Eells-Sampson Type Theorems for Subelliptic Harmonic Maps from Sub- Riemannian Manifolds. The Journal of Geometric Analysis, 31, 3608-3655.
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
[9] 陈恕行. 现代偏微分方程导论[M]. 北京: 科学出版社, 2005.
[10] Gao, L., Lu, L. and Yang, G. (2022) Liouville Theorems of Subelliptic Harmonic Maps. Annals of Global Analysis and Geometry, 61, 293-307.
https://doi.org/10.1007/s10455-021-09811-3
[11] Schmu¨dgen, K. (2012) Unbounded Self-Adjoint Operators on Hilbert Space. Springer Science & Business Media, Berlin.
https://doi.org/10.1007/978-94-007-4753-1

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