AI 中文总结
该研究分析书脊附近密度奇异扰动的开卷结构振动的极限谱问题，刻画耦合宏微观分量的非自伴块算子的谱与Jordan结构，为自伴算子族的极限谱行为提供非平凡实例。
AI 中文摘要
我们研究在书脊附近具有质量密度扰动的开卷结构振动渐近分析中产生的谱问题。极限问题由耦合模型宏观与微观分量的非自伴块算子矩阵支配。我们描述该算子的谱，并完全刻画其特征空间和根子空间。我们进一步证明广义特征向量形成长度至多为2的链，并推导Jordan块存在性及数量的显式判据。该模型提供了一个非平凡例子：作用于不同希尔伯特空间的自伴算子族，其极限谱行为由具有真实Jordan结构的非自伴算子描述。
英文摘要
We investigate the spectral problem arising in the asymptotic analysis of vibrations of open-book structures with a mass density perturbed near the binding. The limiting problem is go\-ver\-ned by a non-self-adjoint block operator matrix coupling the macroscopic and microscopic components of the model. We describe the spectrum of this operator and completely characterize its eigenspaces and root subspaces. We further prove that generalized eigenvectors form chains of length at most two and derive an explicit criterion for the existence and number of Jordan blocks. This model provides a nontrivial example of a family of self-adjoint operators acting in varying Hilbert spaces whose limiting spectral behavior is described by a non-self-adjoint operator with a genuine Jordan structure.
Comments20 pages, 6 figures
