相关论文: Erratum for: Inverse Spectral Theory for a Singula…

We correct an error in the second part of Theorem 3 of our original paper (arXiv:1512.07161).

We develop relative oscillation theory for one-dimensional Dirac operators which, rather than measuring the spectrum of one single operator, measures the difference between the spectra of two different operators. This is done by replacing…

We study spectral subspaces of the Sturm-Liouville operator $f \mapsto -(pf')'$ on $\mathbb{R}$, where $p$ is a positive, piecewise constant function. Functions in these subspaces can be thought of as having a local bandwidth determined by…

This erratum corrects a number of formulae containing mistakes in the paper 'Luminosity function, sizes and FR dichotomy of radio-loud AGN', 2007, MNRAS, v. 381, p.1548. The corrections do not alter any of the conclusions in the original…

The author extends the idea of Jodeit and Levitan for constructing isospectral problems of the classical scalar Sturm-Liouville differential equations to the vectorial Sturm-Liouville differential equations. Some interesting relations are…

We consider the spectral theory for discrete Schr\"odinger operators on the hexagonal lattice and their inverse scattering problem. We give a procedure for reconstructing the compactly supported potential from the scattering matrix for all…

In this paper, the inverse Sturm-Liouville problem with distribution potential and with polynomials of the spectral parameter in one of the boundary conditions is considered. We for the first time prove local solvability and stability of…

The equations in cond-mat/0011020 and Phys. Rev, Lett. 86, 4652 (2001) are valid but a numerical estimate in the paper is incorrect.

It is shown that transfer functions, which play a crucial role in M.G. Krein's study of inverse spectral problems, are a proper tool to formulate local spectral uniqueness conditions.

In this correspondence, it is given a correction to Theorem 4 in Y. Hu, and G. Xiao, "Generalized Self-Shrinking Generator," IEEE Transactions on Information Theory, vol. 50, No. 4, pp. 714-719, April 2004.

We study perturbations of the self-adjoint periodic Sturm--Liouville operator \[ A_0 = \frac{1}{r_0}\left(-\frac{\mathrm d}{\mathrm dx} p_0 \frac{\mathrm d}{\mathrm dx} + q_0\right) \] and conclude under $L^1$-assumptions on the differences…

In this work we study the point spectra of selfadjoint Sturm-Liouville operators with generalized point interactions, where the two one-sided limits of the solution data are related via a general $\mathrm{SL}(2,\mathbb{R})$ matrix. We are…

The operator of double differentiation, perturbed by the composition of the differentiation operator and a convolution one, on a finite interval with Dirichlet boundary conditions is considered. We obtain uniform stability of recovering the…

The work is devoted to the study of Laplace operator when the potential is a singular generalized function and plays the role of a singular perturbation of a Laplace operator. Abstract theorem obtained earlier by the authors B.N. Biyarov…

We correct some oversights in the paper "A spectral sequence for stratified spaces and configuration spaces of points" by the second named author. In particular we explain that an additional hypothesis should be added to Theorem 4.15 in…

This paper develops a methodological framework for addressing a novel and application-oriented inverse nodal problem in Sturm-Liouville operators, having significant applications in seismic wave analysis and submarine underwater radar…

We extend a result of Stolz and Weidmann on the approximation of isolated eigenvalues of singular Sturm-Liouville and Dirac operators by the eigenvalues of regular operators.

We study an indefinite Sturm-Liouville problem due to Richardson whose complicated eigenvalue dependence on a parameter has been a puzzle for decades. In atomic physics a process exists that inverts the usual Schrodinger situation of an…

In this paper, we consider a wave equation on a bounded domain with a Sturm-Liouville operator with a singular intermediate coefficient and a singular potential. To obtain and evaluate the solution, the method of separation of variables is…

This paper presents a systematic study for analytic aspects of discrete spectra methods for convolution of functions supported on disks, according to the Sturm-Liouville theory. We then investigate different aspects of the presented theory…