共查询到20条相似文献,搜索用时 31 毫秒
1.
We study non-self-adjoint second-order differential operators with a constant delay. We establish properties of the spectral characteristics and investigate the inverse problem of recovering operators from their spectra. The uniqueness theorem is proved for this inverse problem. 相似文献
2.
We consider second-order functional differential operators with a constant delay. Properties of their spectral characteristics are obtained and a nonlinear inverse problem is studied, which consists in recovering the operators from their spectra. We establish the uniqueness and develop a constructive algorithm for solution of the inverse problem. 相似文献
3.
V. Yurko 《Applicable analysis》2013,92(1-2):63-77
The inverse spectral problem of recovering pencils of second-order differential operators on the half-line is studied. We give a formulation of the inverse problem, prove the uniqueness theorem and provided a procedure for constructing the solution of the inverse problem. We also establishe connections with inverse problems for partial differential equations. 相似文献
4.
V. Yurko 《Journal of Mathematical Analysis and Applications》2006,320(1):439-463
The inverse spectral problem of recovering pencils of second-order differential operators on the half-line with turning points is studied. We establish properties of the spectral characteristics, give a formulation of the inverse problem, prove a uniqueness theorem and provide a constructive procedure for the solution of the inverse problem. 相似文献
5.
Alexey Fedoseev 《Central European Journal of Mathematics》2013,11(12):2203-2214
We study the inverse problem of recovering Sturm-Liouville operators on the half-line with a Bessel-type singularity inside the interval from the given Weyl function. The corresponding uniqueness theorem is proved, a constructive procedure for the solution of the inverse problem is provided, also necessary and sufficient conditions for the solvability of the inverse problem are obtained. 相似文献
6.
Kazunori Ando 《Annales Henri Poincare》2013,14(2):347-383
We consider the spectral theory and inverse scattering problem for discrete Schrödinger operators on the hexagonal lattice. We give a procedure for reconstructing finitely supported potentials from the scattering matrices for all energies. The same procedure is applicable for the inverse scattering problem on the triangle lattice. 相似文献
7.
Vjacheslav Yurko 《Mathematische Nachrichten》2000,211(1):177-183
We study the inverse problem of recovering differential operators of the Orr‐Sommerfeld type from the Weyl matrix. Properties of the Weyl matrix are investigated, and an uniqueness theorem for the solution of the inverse problem is proved. 相似文献
8.
V. A. Yurko 《Mathematical Notes》2011,89(3-4):438-449
We study the inverse spectral problem for Sturm-Liouville differential operators on hedgehog-type graphs with a cycle and with standard matching conditions at interior vertices. We prove a uniqueness theorem and obtain a constructive solution for this class of inverse problems. 相似文献
9.
Yu Ping Wang 《Results in Mathematics》2013,63(3-4):1131-1144
In this paper, we discuss the inverse problems for Sturm–Liouville operators with boundary conditions polynomially dependent on the spectral parameter. We establish some uniqueness theorems on the potential q(x) for the half inverse problem and the interior inverse problem from spectral data, respectively. 相似文献
10.
V. A. Yurko 《Journal of Mathematical Sciences》2008,150(6):2620-2627
The inverse spectral problem of recovering pencils of second-order differential operators on the half-line with turning points
is studied. We give a formulation of the inverse problem, establish properties of the spectral characteristics, and prove
the uniqueness theorem for the solution of the inverse problem.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 5, pp. 237–246, 2006. 相似文献
11.
V. A. Yurko 《Doklady Mathematics》2010,81(3):410-413
An inverse spectral problem is studied for Sturm-Liouville differential operators on arbitrary compact graphs (spatial networks).
A uniqueness theorem of recovering operators from their spectra is proved, and a constructive procedure for the solution of
the inverse problem is provided. 相似文献
12.
We study the similarity of perturbed compact operators to operators of block-diagonal structure with respect to some family of orthogonal projection operators, which allows us to refine and essentially strengthen results due to R. Turner. We obtain information about the operator realizing the similarity transformation, present estimates for the eigenvalues and eigenvectors of the perturbed operator, and also study the inverse problem of spectral analysis. 相似文献
13.
An inverse nodal problem lies in constructing operators from the given zeros of their eigenfunctions. In this work, we deal with an inverse nodal problem of reconstructing the Dirac system with the spectral parameter in the boundary conditions. We prove that a set of nodal points of one of the components of the eigenfunctions uniquely determines all the parameters of the boundary conditions and the coefficients of the Dirac equations. We also provide a constructive procedure for solving this inverse nodal problem. 相似文献
14.
Anne Boutet de Monvel Iryna Egorova Gerald Teschl 《Journal d'Analyse Mathématique》2008,106(1):271-316
We develop direct and inverse scattering theory for one-dimensional Schrödinger operators with steplike potentials which are asymptotically close to different finite-gap potentials on different half-axes. We give a complete characterization of the scattering data, which allows unique solvability of the inverse scattering problem in the class of perturbations with finite second moment. 相似文献
15.
Mohammed Al Horani 《Journal of Mathematical Analysis and Applications》2010,364(1):204-208
In this paper we study an inverse problem for a degenerate differential equation on a Banach space. A projection method will be used to reduce the problem to a regular abstract inverse problem. To this end some conditions on the operators are assumed to avoid the calculations of some inverses of the involved operators. 相似文献
16.
Andreas Kirsch 《Applicable analysis》2017,96(1):70-84
In this paper, we compare the far-field operators for the full nonlinear inverse scattering problem with the Born approximation as its linearization. The Factorization Method shows that both operators share the same behavior with respect to illposedness of the inverse problem. The results are derived for acoustic and electromagnetic scattering problems and the corresponding problem in electrical impedance tomography. 相似文献
17.
分裂可行问题(SFP)的投影算法 总被引:2,自引:0,他引:2
本文探讨了分裂可行问题(SFP)的投影算法.我们先定义了(SFP)的反问题(ISFP), 然后利用正交投影性质,给出了(SFP)与(ISFP)及某些投影不动点问题之间的关系.随后, 给出了求解(SFP)的几种正交投影算法,其中包括精确和不精确投影格式.基于变分不等式中投影算法收敛性的证明思路和分裂可行问题的特有形式,证明了这几种算法的收敛性.最后通过几个算例对讨论的方法进行了初步比较. 相似文献
18.
M. M. Kokurin 《Russian Mathematics (Iz VUZ)》2013,57(12):16-30
We consider linear fractional differential operator equations involving the Caputo derivative. The goal of this paper is to establish conditions for the unique solvability of the inverse Cauchy problem for these equations. We use properties of the Mittag-Leffler function and the calculus of sectorial operators in a Banach space. For equations with operators in a general form we obtain sufficient conditions for the unique solvability, and for equations with densely defined sectorial operators we obtain necessary and sufficient unique solvability conditions. 相似文献
19.
We investigate a problem for the Dirac differential operators in the case where an eigenparameter not only appears in the
differential equation but is also linearly contained in a boundary condition. We prove uniqueness theorems for the inverse
spectral problem with known collection of eigenvalues and normalizing constants or two spectra. 相似文献
20.
We study the problem of factorisation of non-negative Fredholm operators acting in the Hilbert space L2(0, 1) and its relation to the inverse spectral problem for Bessel operators. In particular, we derive an algorithm of reconstructing
the singular potential of the Bessel operator from its spectrum and the sequence of norming constants. 相似文献