两区间四阶J-对称微分算子J-自伴扩张域的描述
The J-Selfadjoint Realizations of Two-Interval Forth-Order J-Symmetric Operators
DOI: 10.12677/AAM.2017.61010, PDF, HTML, XML, 下载: 1,761  浏览: 2,039  国家自然科学基金支持
作者: 张志敏*, 许美珍:内蒙古工业大学理学院,内蒙古 呼和浩特
关键词: J-对称微分算子J-自伴扩张正则点极限点两区间J-Symmetric Differential Operators J-Selfadjoint Extensions Regular Point limit Point Two-Interval
摘要: 本文利用Hilbert空间上的直和理论刻画了具有正则点和极限点的两区间四阶J-对称微分算子的所有J-自伴扩张。
Abstract: In this paper we characterize all J-selfadjoint extensions for two-interval forth-order J-symmetric differential operators with regular or limit endpoints by the theory of the direct sum in Hilbert spaces.
文章引用:张志敏, 许美珍. 两区间四阶J-对称微分算子J-自伴扩张域的描述[J]. 应用数学进展, 2017, 6(1): 78-89. http://dx.doi.org/10.12677/AAM.2017.61010

参考文献

[1] Knowles, I. (1981) On the Boundary Conditions Characterizing J-Selfadjoint Extensions of J-Symmetric Operators. Journal of Dif-ferential Equations, 40, 193-216.
https://doi.org/10.1016/0022-0396(81)90018-8
[2] Race, D. (1985) The Theory of J-Selfadjoint Extensions of J-Symmetric Operators. Journal of Differential Equations, 57, 258-274.
https://doi.org/10.1016/0022-0396(85)90080-4
[3] Glazman, I.M. (1957) An Analogue of the Extension Theory of Hermitian Operators and a Non-Symmetric One-Dimensional Boundary Problem on a Half-Axis. Doklady Akademii Nauk SSSR, 115, 214-216.
[4] Galindo, A. (1962) On the Existence of J-Selfadjoint Extensions of J-Symmetric Operators with Adjoint. Communi-cations on Pure and Applied Mathematics, 15, 423-425.
https://doi.org/10.1002/cpa.3160150405
[5] Knowles, I. (1980) On J-Selfadjoint Extensions of J-Symmetric Operators. Proceedings of the American Mathematical Society, 79, 42-44.
https://doi.org/10.2307/2042383
[6] Zhikhar, N.A. (1959) The Theory of Extensions of J-Symmetric Operators. Ukrains' kyi Matematychnyi Zhurnal, 11, 352-364.
[7] 刘景麟. 关于J-对称算子的自伴延拓[J]. 内蒙古大学学报(自然科学版), 1992, 23(3): 312-316.
[8] Shang, Z. (1988) On J-Selfadjoint Extensions of J-Symmetric Ordinary Differential Operators. Journal of Differential Equations, 73, 153-177.
https://doi.org/10.1016/0022-0396(88)90123-4
[9] 尚在久. 关于J-对称微分算子的J-自伴扩张的若干注记[J]. 数学学报, 1996, 39(3): 387-395.
[10] Naimark, M.A. (1954) Linear Differential Operators. GITTI, Moscow.
[11] Cao, Z. (1985) On Self-Adjoint Extensions of n-th Order Differential Operators in the Limit Circle Case. Acta Mathematocs Sinica, 28, 205-217.
[12] Sun, J. (1986) On the Self-Adjoint Extensions of Symmetric Ordinary Differential Operators with Middle Deficiency Indices. Acta Mathematica Sinica, 2, 152-167.
https://doi.org/10.1007/BF02564877
[13] Everitt, W.N. and Zettl, A. (1986) Sturm-Liouville Differential Operators in Direct Sum Spaces. Rocky Mountain Journal of Mathematics, 16, 497-516.
https://doi.org/10.1216/RMJ-1986-16-3-497
[14] Zettl, A. (2005) Sturm-Liouville Theory. American Mathematical Socie-ty.
[15] Wang, A., Sun, J. and Zettl, A. (2007) Two-Interval Sturm-Liouville Operators in Modified Hilbert Spaces. Journal of Ma-thematical Analysis and Applications, 328, 390-399.
https://doi.org/10.1016/j.jmaa.2006.05.058
[16] Sun, J., Wang, A. and Zettl, A. (2007) Two-Interval Sturm-Liouville Operators in Direct Sum Spaces with Inner Product Multiples. Results in Mathematics, 50, 155-168.
https://doi.org/10.1007/s00025-006-0241-1
[17] Suo, J. and Wang, W. (2012) Two-Interval Even Order Differential Operators in Direct Sum Spaces. Results in Mathematics, 62, 13-32.
https://doi.org/10.1007/s00025-011-0126-9