Parametrization of the isospectral set for the vector-valued Sturm-Liouville problem
Dmitry Chelkak, Evgeny Korotyaev
我们得到了有限区间上向量值Sturm-Liouville问题的矩阵值位势的等谱集的参数化。
We obtain a parametrization of the isospectral set of matrix-valued potentials for the vector-valued Sturm-Liouville problem on a finite interval.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
On the Construction of Isospectral Vectorial Sturm-Liouville Differential Equations
本文将Jodeit和Levitan构造经典标量Sturm-Liouville微分方程等谱问题的思想推广到向量Sturm-Liouville微分方程.发现了一些有趣的关系。
A quantitative version of Gordon's Theorem for Jacobi and Sturm-Liouville operators
本文证明了关于Jacobi矩阵和Sturm-Liouville算子特征值缺失的Gordon定理的一个定量形式。
A connection, which shows the dependence of norming constants on boundary conditions, was found using the Gelfand-Levitan method for the solution of inverse Sturm-Liouville problem.
Sturm-Liouville operators with measure-valued coefficients
我们给出了一个全面的处理Sturm-Liouville算子的测度值系数，包括充分讨论自伴扩张和边界条件，预解式，和Weyl-Titchmarsh理论。我们避免了以前的技术限制，并在同一时间，扩大所有的结果到更大的一类运营商。我们的算子包括经典的Sturm-Liouville算子、在处理Camassa-Holm方程时产生的Lax算子、Jacobi算子和作为特例的时间尺度上的Sturm-Liouville算子。
On the Absolutely Continuous Spectrum of Sturm-Liouville Operators with Applications to Radial Quantum Trees
我们考虑标准从属理论一般Sturm-Liouville算子，并给出标准时的有界性的解决方案意味着没有从属的解决方案存在。作为应用，我们证明了一般Sturm-Liouville算子的Weidmann型结果，并研究了径向对称量子树的绝对连续谱。
Relative Oscillation Theory for Sturm-Liouville Operators Extended
我们将相对振动理论推广到Sturm-Liouville算子$H u = r^{-1}(-(pu')'+q u)$具有不同$p$的情形.我们证明了某些解的Wronskians零点的加权数等于Krein谱移函数在本质谱隙内的值。
Uniqueness for Inverse Sturm-Liouville Problems with a Finite Number of Transmission Conditions
我们建立了各种唯一性结果的Sturm-Liouville算子的逆谱问题的有限数量的不连续性在内点，我们施加通常的传输条件。我们考虑的情况下，经典罗宾和特征参数依赖的边界条件。
Sturm-Liouville problems on graphs with Robin boundary conditions
本文研究了带有Robin边界条件的图上Sturm-Liouville问题，探讨了特征值的渐进行为及通过已知图结构和特征值恢复边界条件系数的方法。
We consider Sturm-Liouville operators with measure-valued weight and potential, and positive, bounded diffusion coefficient which is bounded away from zero. By means of a local periodicity condition, which can be seen as a quantitative Gordon condition, we prove a bound on eigenvalues for the corresponding operator in $L_p$, for $1\leq p<\infty$. We also explain the sharpness of our quantitative bound, and provide an example for quasiperiodic operators.
Ambarzumyan Type Theorem for a matrix quadratic Sturm-Liouville equation with energy dependent
将二次Sturm-Liouville问题的Ambarzumyan定理推广到d维二阶微分系统。证明了如果谱与属于零势的谱相同，则矩阵值函数p和q都为零
Inverse spectral problems for energy-dependent Sturm-Liouville equations
研究了由能量依赖的Sturm-Liouville方程的Dirichlet谱和赋范常数序列重构该方程的逆谱问题。对于这类问题，我们给出了相应的光谱数据的完整描述，提出了重建算法，并建立了重建的唯一性。该方法是基于能量相关的Sturm-Liouville方程和特殊形式的Dirac算子的谱问题之间的连接。
Lower bounds for self-adjoint Sturm-Liouville operators
本研究针对加权L²希尔伯特空间中三系数Sturm-Liouville微分表达式对应的自伴算子，给出其下界的估计结果。
Analyticity and uniform stability of the inverse singular Sturm--Liouville spectral problem
我们证明了Sturm-Liouville算子的势解析地和Lipschitz连续地依赖于谱数据（两个谱或一个谱和相应的赋范常数）。本文讨论Sobolev类W^{s-1}_2（0，1），s \in [0，1]中具有实值分布势的算子类.
Resolvent convergence of Sturm-Liouville operators with singular potentials
本文考虑希尔伯特空间$L_2$中的Sturm-Liuoville算子，其奇异复位势为$W^{-1}_2$，边界条件为两点.对于这类算子，我们给出了同类算子逼近范数预解式的充分条件。
This work deals with an inverse problem for the Sturm-Liouville operator with non-separated boundary conditions, one of which linearly depends on a spectral parameter. Uniqueness theorem is proved, solution algorithm is constructed and sufficient conditions for solvability of inverse problem are obtained. As spectral data, we only use the spectrum of one boundary value problem and some sequence of signs.
Inverse scattering on the line for the matrix Sturm-Liouville equation
研究了直线上矩阵Sturm-Liouville方程的逆散射问题。得到了散射数据的充要条件。
Sturm-Liouville operators on time scales
建立了时间尺度上的Sturm-Liouville方程与测度系数的Sturm-Liouville方程之间的联系。在此基础上，我们推广了过去不同作者关于时间尺度上Sturm-Liouville方程的几个结果.
In this study, we give the Sturm comparison theorems for discrete fractional Sturm-Liouville (DFSL) equations within Riemann-Liouville and Grünwald-Letnikov sense. The emergence of Sturm-Liouville equations began as one dimensional Schrödinger equation in quantum mechanics and one of the most important results is Sturm comparison theorems [27]. These theorems give information about the properties of zeros of two equations having different potentials.
Selfadjoint and $m$ sectorial extensions of Sturm-Liouville operators
在微分表达式系数的极小光滑条件下，刻画了强制Sturm-Liouville算子的自伴扩张和$m$ -扇形扩张.
The inverse spectral problems are studied for the Sturm-Liouville operator on the star-shaped graph and for the matrix Sturm-Liouville operator with the boundary condition in the general self-adjoint form. We obtain necessary and sufficient conditions of solvability for these two inverse problems, and also prove their local solvability and stability.
We consider Sturm-Liouville operators with singular potentials from the class on star-type graph with cycle, which consist the edges with commensurable lengths. Asymptotic representation for eigenvalues for such operators is obtained. Recovering of the characteristic function the Sturm-Liouville operators with the singular potentials is considered.
Inverse spectral problems for Sturm-Liouville operators with singular potentials, II. Reconstruction by two spectra
解决了由两个谱恢复Sturm-Liouville算子奇异势$q\in W^{-1}_{2}(0,1)$的逆谱问题。给出了重建算法，并给出了Sturm-Liouville算子谱数据的充要条件。
Spectral properties of Sturm-Liouville equations with singular energy-dependent potentials
研究了能量依赖的Sturm-Liouville方程的谱性质，引入了赋范常数的概念，建立了赋范常数与谱的关系。其中一个主要的工具是线性化的问题在一个合适的庞特里亚金空间。
The regularized trace formula for the Sturm-Liouville equation with spectral parameter in the boundary conditions
得到了在边界条件下带谱参数的Sturm-Liouville方程的一阶正则迹公式。
A priori bounds and existence of non-real eigenvalues of indefinite Sturm-Liouville problems
本文给出了正则不定Sturm-Liouville问题的可能非实特征值的先验界，并得到了这类问题允许非实特征值存在的充分条件.
In this paper, we consider an interior inverse Sturm-Liouville problem on time scale T and give a Mochizuki-Trooshin type theorem.
We prove Marchenko-type uniqueness theorems for inverse Sturm-Liouville problems. Moreover, we prove a generalization of Ambarzumyans theorem.
On Properties of the Sturm-Liouville Operator with Degenerate Boundary Conditions
本文研究了具有任意复值位势q（x）和退化边界条件的Sturm-Liouville算子的谱问题.我们求解了相应的反问题，并研究了根函数系的完备性和基的性质。
On an inverse problem for Sturm-Liouville equation
本文证明了具有间断系数的Sturm-Liouville算子反问题可解的充要条件定理，并给出了由谱数据（特征值和归一化数）重构位势的算法。
Eigenvalues of Sturm Liouville problems with discontinuity conditions inside a finite interval
在这项工作中，我们使用\textit{regularized sampling method}来计算Sturm-Liouville问题的特征值与间断条件在有限的时间间隔内。通过计算几个本征值及其对应的本征函数，给出了一个例子。
In this study, we define discrete fractional Sturm-Liouville (DFSL) operators within Riemann-Liouville and Grünwald-Letnikov fractional operators with both delta and nabla operators. We show selfadjointness of the DFSL operator for the first time and prove some spectral properties, like orthogonality of distinct eigenfunctions, reality of eigenvalues, paralelly in integer and fractional order differential operator counterparts.
On The Eigenvalues of Some Vectorial Sturm-Liouville Eigenvalue Problems
本文试图导出某些向量Sturm-Liouville微分方程的大特征值的渐近表达式。得到了直到$O(1/n)$项的大特征值平方根公式的精确描述。
Erratum for: Inverse Spectral Theory for a Singular Sturm-Liouville Operator on [0,1]
这是对我们在《微分方程杂志》第76卷（1988年）中的文章的更正。
Estimates on the non-real eigenvalues of regular indefinite Sturm-Liouville problems
具有不定权函数的正则Sturm-Liouville问题可能具有多个非实特征值。本文证明了这些特征值的实部和虚部的显式界。
An inverse spectral problem is studied for the matrix Sturm-Liouville operator on a finite interval with the general self-adjoint boundary condition. We obtain a constructive solution based on the method of spectral mappings for the considered inverse problem. The nonlinear inverse problem is reduced to a linear equation in a special Banach space of infinite matrix sequences. In addition, we apply our results to the Sturm-Liouville operator on a star-shaped graph.
Reconstruction of energy-dependent Sturm-Liouville equations from two spectra
本文研究了由两个谱重构能量相关的Sturm-Liouville方程的逆谱问题。我们给出了一个重建算法，并证明了重建的存在性和唯一性。我们的方法基本上利用了研究中的谱问题和特殊形式的狄拉克算子之间的联系。
An application of the fixed point theorem to the inverse Sturm-Liouville problem
本文考虑了$[0,1]$上的Sturm-Liouville算子$-y''+v(x)y$，其Dirichlet边界条件为$y(0)=y(1)=0$ .对于任何$1\le p<\infty$，我们给出了对应于$v\in L^p(0,1)$的谱数据的特征定理的一个简短证明.
Inverse problems of spectral analysis for the Sturm-Liouville operator with regular boundary conditions
考虑Sturm-Liouville算子Lu= u“-q（x）u具有正则但非强正则边界条件.在一些补充的假设下，我们证明了在可和函数空间中，保证渐近多重谱的势集q（x）处处稠密.
We study Sturm--Liouville differential operators on the time scales consisting of a finite number of isolated points and segments. In a previous paper it was established that such operators are uniquely determined by their spectral characteristics. In the present paper, an algorithm for their recovery based on the method of spectral mappings is obtained. We also prove that the eigenvalues of two Sturm--Liouville boundary value problems with one common boundary condition alternate.
On the Basis Property of the Root Functions of Sturm-Liouville Operators with General Regular Boundary Conditions
得到了Sturm-Liouville算子在一般正则边界条件下本征值和本征函数的渐近公式。利用这些公式，我们找到了关于势q的充分条件，使得这些算子的根函数不形成Riesz基。
Inequalities among eigenvalues of different self-adjoint discrete Sturm-Liouville problems
本文建立了不同自伴离散Sturm-Liouville问题的特征值之间的不等式。对于固定的离散Sturm-Liouville方程，给出了不同边界条件下特征值之间的不等式.对于固定的边界条件，给出了不同方程的特征值之间的不等式。这些结果是通过应用第n个特征值函数的连续性和不连续性、第n个特征值函数在某个方向上的单调性以及边界条件空间中的自然环得到的。所得结果推广了已有的关于不同Sturm-Liouville问题特征值间不等式的相关结果。
The inverse spectral problem is studied for the Sturm-Liouville operator with a complex-valued potential and arbitrary entire functions in one of the boundary conditions. We obtain necessary and sufficient conditions for uniqueness, and develop a constructive algorithm for the inverse problem solution. The main results are applied to the Hochstadt-Lieberman half-inverse problem. As an auxiliary proposition, we prove local solvability and stability for the inverse Sturm-Liouville problem by the Cauchy data in the non-self-adjoint case.
On the Basis Property of the Root Functions of Some Class of Non-self-adjoint Sturm--Liouville Operators
得到了Sturm-Liouville算子在某些正则边界条件下本征值和本征函数的渐近公式。利用这些公式，我们找到了关于势q的充分条件，使得这些算子的根函数不形成Riesz基。
We consider the inverse Sturm-Liouville problem with one discontinuous point on three-star graph, we deduced the distribution of the eigenvalues, and proved that one spectrum could uniquely determine the unknown potential and jump information when we know the whole potentials on two edges and half potential on another edge.
On the basis property of the root function systems of regular boundary value problems for the Sturm-Liouville operator
考虑非自伴Sturm-Liouville算子Lu= u“-q（x）u具有正则但非强正则边界条件，其中q（x）是任意复值可和函数.我们研究了上述算子的根函数系的基性质。
Spectral Analysis for the Matrix Sturm-Liouville Operator on a Finite Interval
研究了有限区间上矩阵Sturm-Liouville方程的逆谱问题。给出了谱特征的性质，构造了反问题的求解方法，并给出了反问题可解的充要条件.
The matrix Sturm-Liouville operator on a finite interval with the boundary conditions in the general self-adjoint form and with the singular potential from the class $W_2^{-1}$ is studied. This operator generalizes Sturm-Liouville operators on geometrical graphs. We investigate structural and asymptotical properties of the spectral data (eigenvalues and weight matrices) of this operator. Furthermore, we prove the uniqueness of recovering the operator from its spectral data, by using the method of spectral mappings.
Uniform stability of recovering the Sturm-Liouville operators with frozen argument
本文研究从谱及附加数据反演具有冻结变量的Sturm-Liouville算子，证明势函数对输入数据具有Lipschitz连续依赖的一致稳定性。
Inverse Spectral Problems for Sturm-Liouville Operators on Hedgehog-type Graphs with General Matching Conditions
研究了具有一般匹配条件的Sturm-Liouville微分算子在刺猬型图上的边值问题.研究了从谱数据中恢复微分方程系数的逆谱问题。对于这个反问题，我们证明了一个唯一性定理，并提供了一个程序来构建其解决方案。
An inverse spectral problem for the matrix Sturm-Liouville operator on the half-line
考虑了在射线上具有可积势的矩阵Sturm-Liouville算子。我们研究的逆谱问题，其中包括在恢复这个运营商的Weyl矩阵。本文的主要结果是非自伴随矩阵Sturm-Liouville算子的Weyl矩阵的充要条件。我们还调查了自伴的情况下，并获得的谱数据的表征作为我们的一般结果的推论。
Inverse spectral problem of Sturm-Liouville equation with many frozen arguments
本文研究具有多个冻结参数的Sturm-Liouville算子的反谱问题，在假设条件下证明唯一性定理，并给出数值模拟。
On some class of singular Sturm-Liouville problems
研究了方程$-(y'/r)'+qy=λpy$的Sturm-Liouville谱问题，其中广义函数为$r\ge 0$，$q$和$p$.结果表明，该问题可以归结为与$r\equiv 1$类似的问题。考虑$q=0$和自相似$r$和$p$的情况作为示例。
Computing the spectrum of non self-adjoint Sturm-Liouville problems with parameter dependent boundary conditions
本文讨论了用\textit{regularized sampling method}计算具有参数依赖边界条件的非自伴Sturm-Liouville问题的特征值。文中给出了几个数值算例，其中包括奇异值的计算，以说明本方法的优点，并与可用的精确特征值进行了比较。
On the Nonself-adjoint Sturm-Liouville Operator with Matrix Potential
本文给出了具有可和系数和拟周期边界条件的Sturm-Liouville方程组生成的非自伴随算子的本征值和本征函数的渐近公式。然后利用这些渐近公式，我们找到了该算子的根函数形成Riesz基的势的条件。
Asymptotic properties of eigenvalues and eigenfunctions of a Sturm-Liouville problem with discontinuous weight function
本文利用[O. Sh. Mukhtarov和M. Kadakal，Some spectral properties of one Sturm-Liouville type problem with discontinuous weight，Siberian Mathematical Journal，46（2005）681-694]我们将正则Sturm-Liouville问题的一些谱性质推广到由在两个内点具有不连续权的Sturm-Liouville方程以及谱参数依赖边界条件组成的那些问题。我们给出了所考虑的问题的算子理论的制定，并获得渐近公式的特征值和特征函数。
Uniform stability of the inverse Sturm-Liouville problem on a star-shaped graph
本文研究了星形图上逆斯图尔姆-刘维尔问题的均匀稳定性，通过谱数据恢复势函数并证明其稳定性。
We introduce a novel approach for dealing with eigenvalue problems of Sturm-Liouville operators generated by the differential expression \begin{equation*} Ly=\frac{1}{r}\left( -(p\left[ y^{\prime }+sy\right] )^{\prime }+sp\left[ y^{\prime }+sy\right] +qy\right) \end{equation*} which is based on norm resolvent convergence of classical Sturm-Liouville operators. This enables us to describe the continuous dependence of the $n$-th eigenvalue on the space of self-adjoint boundary conditions and the coefficients of the differential equation after giving the inequalities among the eigenvalues. Moreov…
Reconstruction techniques for inverse Sturm-Liouville problems with complex coefficients
本文针对复值势函数的逆 Sturm-Liouville 问题，提出基于 Bessel 函数 Neumann 级数表示的统一直接数值方法，可同时恢复势函数与边界条件，具备高效精度控制，且仅需求解线性代数方程组。
We consider the non-self-adjoint Sturm-Liouville operator on a finite interval. The inverse spectral problem is studied, which consists in recovering this operator from its eigenvalues and generalized weight numbers. We prove local solvability and stability of this inverse problem, relying on the method of spectral mappings. Possible splitting of multiple eigenvalues is taken into account.
In this paper, we present a new approachment for Sturm-Liouville problem having special potentials. We acquire the representations of solutions and asymptotic formulas for solutions with regard to initial conditions. Also, a few applications are given to show the requirement of Sturm-Liouville difference equations having potential function in view of suitability to the spectral theory. The approximate numerical outcomes for the eigenfunctions are compared with each other.
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。