Dissipative operators, symplectic geometry, and limit-circle solutions

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• 作者：Siqin Yao^a ; ^{siqin@imu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Jiong Sun^a ; ^{masun@imu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Anton Zettl^b ; ^{zettl@msn.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Dissipative extensions ; Symplectic geometry ; Dissipative subspaces ; Limit-circle solutions ; Boundary conditions
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：445
• 期：1
• 页码：746-761
• 全文大小：356 K

文摘

For a general symmetric ordinary differential expression M and a positive weight function w, the authors characterized the dissipative and strictly dissipative extensions of the minimal operator generated by M in terms of subspaces of a symplectic geometry space. Here we characterize these subspaces in terms of LC solutions, namely, we characterize the boundary conditions of the dissipative and strictly dissipative extensions by LC solutions in a Hilbert space.