Please wait a minute...
Frontiers of Mathematics in China

ISSN 1673-3452

ISSN 1673-3576(Online)

CN 11-5739/O1

邮发代号 80-964

2019 Impact Factor: 1.03

Frontiers of Mathematics in China  2022, Vol. 17 Issue (6): 1025-1035   https://doi.org/10.1007/s11464-022-1032-z
  本期目录
J-selfadjointness of a class of high-order differential operators with transmission conditions
Ji LI, Meizhen XU()
School of Sciences, Inner Mongolia University of Technology, Hohhot 010051, China
 全文: PDF(507 KB)   HTML
Abstract

This paper is to investigate the J-selfadjointness of a class of high-order complex coefficients differential operators with transmission conditions. Using the Lagrange bilinear form of J-symmetric differential equations, the definition of J-selfadjoint differential operators and the method of matrix representation, we prove that the operator is J-selfadjoint operator, and the eigenvectors and eigen-subspaces corresponding to different eigenvalues are C-orthogonal.

Key wordsHigh-order differential operator    transmission conditions    J-selfadjoint    C-orthogonal
出版日期: 2023-01-04
Corresponding Author(s): Meizhen XU   
 引用本文:   
. [J]. Frontiers of Mathematics in China, 2022, 17(6): 1025-1035.
Ji LI, Meizhen XU. J-selfadjointness of a class of high-order differential operators with transmission conditions. Front. Math. China, 2022, 17(6): 1025-1035.
 链接本文:  
https://academic.hep.com.cn/fmc/CN/10.1007/s11464-022-1032-z
https://academic.hep.com.cn/fmc/CN/Y2022/V17/I6/1025
1 J J Ao, J Sun, M Z Zhang. The finite spectrum of Sturm-Liouville problems with transmission conditions. Appl Math Comput 2011; 218(4): 1166–1173
2 A Galindo. On the existence of J-selfadjoint extensions of J-symmetric operators with adjoint. Comm Pure Appl Math 1962; 15: 423–425
3 I Knowles. On J-selfadjoint extensions of J-symnnetric operators. Proc Amer Math Soc 1980; 79(1): 42–44
4 I Knowles. On the boundary conditions characteriizing J-selfadjoint extensions of J-symmetric operators. J Differential Equations 1981; 40(2): 193–216
5 J Li, M Z Xu, B S Fan. J-self-adjointness of a class of second order differential operators with transmission conditions. Jounal of Inner Mongolia University of Technology 2020; 39(5): 327–331
6 J L Liu. On J selfadjoint extensions of J symmetric operators. J Inn Mong Univ Nat Sci 1992; 23(3): 312–316
7 D Mu, J Sun, S Q Yao. Asymptotic behaviors and Green’s function of two-interval Sturm-Liouville problems with transmission conditions. Math Appl (Wuhan) 2014; 27(3): 658–672
8 D Race. The spectral theory of complex Sturm-Lioluville operators. Ph D Thesis, Johannesburg: University of the Witwatersrand, 1980
9 D Race. The theory of J-selfadjoint extensions of J-symmetric operators. J Differential Equations 1985; 57(2): 258–274
10 Z J Shang. On J-selfadjoint extensions of J-symmetric ordinary differential operators. J Differ Equ 1988; 73(1): 153–177
11 A P Wang, J Sun, A Zettl. Two-interval Sturm-Liouville operators in modified Hilbert spaces. J Math Anal Appl 2007; 328(1): 390–399
12 Z WangS Z Fu. Spectral Theory of Linear Operators and Its Applications. Beijing: Science Press, 2013 (in Chinese)
13 X Y Zhang, J Sun. A Class of 2nth-order differential operator with eigenparameter-dependent boundary and transmission conditions. Miskolc Math Note 2013; 14(1): 355–372
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed