Solvability and stability of the inverse problem for the quadratic differential pencil

An inverse spectral problem for second-order functional-differential pencils with two delays

We consider a second order functional-differential pencil with two constant delays of the argument and study the inverse problem of recovering its coefficients from the spectra of two boundary value problems with one common boundary condition. The uniqueness theorem is proved and a constructive procedure for solving this inverse problem along with necessary and sufficient conditions for its solvability is obtained. Moreover, we give a survey on the contemporary state of the inverse spectral theory for operators with delay. The pencil under consideration generalizes Sturm-Liouville-type operato…

差分方程的二次束：Jost解、谱和主向量

Quadratic pencil of difference equations: Jost solutions, spectrum, and principal vectors

本文利用Schr dinger型差分算子$L_λ$的二次束，对二阶非自伴差分方程的谱分析进行了研究.通过引入Jost型解，分析了算子$L_λ$的谱的结构和数量性质，从而得到了Degasperis（\emph{J.Math.Phys} . 11：551- 567，1970）和Bairamov et.等人，（\emph{Quaest. Math.} 26：15- 30，2003）开发的。此外，几个类比之间的差异和$q$ -差异的情况下建立。最后，引入了$L_λ$的主向量，为谱展开奠定了基础。数学学科分类（2000年）：39 A10、39 A12、39 A13

A factorization of a quadratic pencils of accretive operators and applications

A canonical factorization is given for a quadratic pencil of accretive operators in a Hilbert space. Also, we establish some relationships between an m-accretive operator and its Moore-Penorse inverse. As an application, we study a result of existence, uniqueness, and maximal regularity of the strict solution for complete abstract second order differential equation in the non-homogeneous case. The paper is concluded with some questions left open from the preceding discussions.

The Moore-Penrose inverse of accretive operators with application to quadratic operator pencils

We establish some relationships between an m-accretive operator and its Moore-Penorse inverse. We derive some perturbation result of the Moore-Penorse inverse of a maximal accretive operator. As an application we give a factorization theorem for a quadratic pencil of accretive operators. Also, we study a result of existence, uniqueness, and maximal regularity of the strict solution for complete abstract second order differential equation. Illustrative examples are also given.

带冻结自变量的微分束的逆谱问题

Inverse spectral problem for differential pencils with a frozen argument

本文研究带冻结自变量的微分束的逆谱问题，推导谱问题的主方程及精细结构，分退化与非退化情形证明逆问题唯一性，给出势函数重构方法及可解性充要条件。

On a one-dimensional quadratic operator pencil with a small periodic perturbation

We consider a quadratic operator pencil with a small periodic perturbation multiplied by the spectral parameter. It is motivated, in particular, by a one-dimensional Klein-Gordon equation with a time-parity-symmetric perturbation. We study in details the structure of the considered operator pencil. We show that its essential spectrum has a band structure and at certain thresholds, the bands bifurcate into small parabolas. We then study how the isolated limiting eigenvalues behave under the perturbation. We show that if zero is a limiting isolated eigenvalue, under the perturbation it remains a…

Schrodinger算子及其双曲束

Schrodinger operators and associated hyperbolic pencils

对于一大类Schrodinger算子，我们通过使耦合常数以非常特殊的方式依赖于能量，引入了双曲二次束。对于这些铅笔，散射理论的许多问题都更容易研究。然后，我们给出了一些应用到原来的薛定谔算子。

On one inverse problem

The stated paper is dedicated to one of the inverse problems of spectral theory. It is necessary to define matrix (constant) coefficients of some quadratic pencil, if the eigenvalues of this pencil are known. Furthermore, it is known that these eigenvalues are complex valued and besides that they contain their conjugate ones. As is known, it is a problem of one company. We shall approach this problem on some restrictions.

Operator Pencils and Half-range Problem in Operator Theory

This article can be considered as the first version of a book which the author plans to write about half-range problems in operator theory. It consists of two parts. The first part is based on lectures which the author delivered at University of Calgary and Lomonosov Moscow State University. The main attention in this part is paid to the selection of waves which are involved in the formulation of the Mandelstamm radiation principle (the eigen-pairs, corresponding to the real eigenvalues) and to the factorization problems of self-adjoint and dissipative, quadratic and polynomial operator pencil…

二次矩阵束的一组完全溶剂对

A complete pair of solvents of a quadratic matrix pencil

本文研究二次矩阵束微分方程，利用完全溶剂对将初值问题化为两个矩阵指数计算，并讨论如何选取可减小舍入误差的完全溶剂对。

具有伪各向同性结构的半圆柱的稳态振荡

Steady state oscillations of a half cylinder with a pseudo isotropic structure

本文针对含伪各向同性弹性结构的半无限圆柱振荡问题，研究其变量分离后得到的自伴二次 pencil 的谱性质。