On Factorization of a Perturbation of a J-selfadjoint Operator Arising in Fluid Dynamics

论非自伴Sturm-Liouville算子非局部扰动的恢复

On recovering non-local perturbation of non-selfadjoint Sturm-Liouville operator

本文研究非自伴Sturm-Liouville算子非局部扰动的逆谱问题，针对已知p的情形，通过建立特征函数与位势系数的关系，得到谱的充要条件，指出部分谱无信息，补充最小系数数据后证明了逆问题的唯一性并给出算法。

Factorization theorem for the transfer function of a 2x2 operator matrix with unbounded couplings

We consider the analytic continuation of the transfer function associated with a 2x2 operator matrix having unbounded couplings into unphysical sheets of its Riemann surface. We construct a family of non-selfadjoint operators which factorize the transfer function and reproduce certain parts of its spectrum including the nonreal (resonance) spectrum situated in the unphysical sheets neighboring the physical sheet.

Spectra for semiclassical operators with periodic bicharacteristics in dimension two

We study the distribution of eigenvalues for selfadjoint $h$--pseudodifferential operators in dimension two, arising as perturbations of selfadjoint operators with a periodic classical flow. When the strength $\varepsilon$ of the perturbation is $\ll h$, the spectrum displays a cluster structure, and assuming that $\varepsilon \gg h^2$ (or sometimes $\gg h^{N_0}$, for $N_0 >1$ large), we obtain a complete asymptotic description of the individual eigenvalues inside subclusters, corresponding to the regular values of the leading symbol of the perturbation, averaged along the flow.

The spectral form of the functional model for maximally dissipative operators: A Lagrange identity approach

The spectral and scattering properties of non-selfadjoint problems pose a mathematical challenge. Apart from exceptional cases, the well-developed methods used to examine the spectrum of selfadjoint problems are not applicable. One of the tools to attack non-selfadjoint problems are functional models. A drawback of many functional models is that their constructions require objects which may be difficult to describe explicitly, such as operator square roots, making it hard to apply the results to specific examples. We develop a functional model for the case when the non-selfadjointness arises b…

无界算子的特征值渐近性。双光子量子 Rabi 模型

Eigenvalues asymptotics of unbounded operators. Two-photon quantum Rabi model

本文研究无界算子在紧、相对紧及非紧等扰动下的特征值渐近性，推广 Janas-Naboko 引理，并以双光子量子 Rabi 模型为例给出能量算子大特征值三项渐近公式及相关多项式渐近性。

Operator interpretation of resonances arising in spectral problems for 2 x 2 operator matrices

We consider operator matrices {\bf H}= (A_0 B_{01} \\ B_{10} A_{1}) with self-adjoint entries A_i, i=0,1, and bounded B_{01}=B_{10}^*, acting in the orthogonal sum {\cal H}={\cal H}_0\oplus{\cal H}_1 of Hilbert spaces {\cal H}_0 and {\cal H}_1. We are especially interested in the case where the spectrum of, say, A_1 is partly or totally embedded into the continuous spectrum of A_0 and the transfer function M_1(z)=A_1-z+V_1(z), where V_1(z)=B_{10}(z-A_0)^{-1}B_{01}, admits analytic continuation (as an operator-valued function) through the cuts along branches of the continuous spectrum of the en…