Related papers: Recovering First Order Integro-Differential Operat…
In this note, we solve an inverse spectral problem for a class of finite band symmetric matrices. We provide necessary and sufficient conditions for a matrix valued function to be a spectral function of the operator corresponding to a…
A formal fourth order differential operator with a singular coefficient that is a linear combination of the Dirac delta-function and its derivatives is considered. The asymptotic behavior of spectra and eigenfunctions of a family of…
In their work on differential operators in positive characteristic, Smith and Van den Bergh define and study the derived functors of differential operators; they arise naturally as obstructions to differential operators reducing to positive…
We provide an abstract framework for singular one-dimensional Schroedinger operators with purely discrete spectra to show when the spectrum plus norming constants determine such an operator completely. As an example we apply our findings to…
A third order self-adjoint differential operator with periodic boundary conditions and an one-dimensional perturbation has been considered. For this operator, we first show that the spectrum consists of simple eigenvalues and finitely many…
In this article we consider a class of integrable operators and investigate its connections with the following theories:the spectral theory of non-self-adjoint operators, the Riemann-Hilbert problem, the canonical differential systems and…
Let $$L_0=\suml_{j=1}^nM_j^0D_j+M_0^0,\,\,\,\,D_j=\frac{1}{i}\frac{\pa}{\paxj}, \quad x\in\Rn,$$ be a constant coefficient first-order partial differential system, where the matrices $M_j^0$ are Hermitian. It is assumed that the homogeneous…
Scattering problem for a self-adjoint integro-differential operator, which is the sum of the operator of second derivative and of a finite-dimensional self-adjoint operator, is studied. Jost solutions are found and it is shown that the…
The Jacobi matrices with bounded elements whose spectrum of multiplicity 2 is separated from its simple spectrum and contains an interval of absolutely continuous spectrum are considered. A new type of spectral data, which are analogous for…
The inverse problem for the Sturm- Liouville operator with complex periodic potential and positive discontinuous coefficients on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the…
For a large class of integral operators or second order differential operators, their isospectral (or cospectral) operators are constructed explicitly in terms of $h$-transform (duality). This provides us a simple way to extend the known…
We solve the inverse spectral problem of recovering the singular potentials $q\in W^{-1}_{2}(0,1)$ of Sturm-Liouville operators by two spectra. The reconstruction algorithm is presented and necessary and sufficient conditions on two…
In this paper, we establish a condition on the coefficients of differential operators generated in the space of square-integrable functions on the entire real line by an ordinary differential expression with periodic, complex-valued…
Spectrum of a certain class of first order conformally invariant operators on the sphere is explicitly computed. The class contains the (elliptic verions of) Rarita-Schwinger operator and its higher spin analogues.
Inverse spectral problems consist in recovering operators by their spectral characteristics. The problem of recovering the Sturm-Liouville operator with one frozen argument was studied earlier in works of various authors. In this paper, we…
We develop the method of similar operators to study the spectral properties of unbounded perturbed linear operators that can be represented by matrices of various kinds. The class of operators under consideration includes various…
We investigate the problem of the existence of first integrals for multidimensional and ordinary linear differential systems with constant coefficients. The spectral method of the first integrals basis construction for these systems of…
Multiple scalar integral representations for traces of operator derivatives are obtained and applied in the proof of existence of the higher order spectral shift functions.
Spectral operators of matrices proposed recently in [C. Ding, D.F. Sun, J. Sun, and K.C. Toh, Math. Program. {\bf 168}, 509--531 (2018)] are a class of matrix valued functions, which map matrices to matrices by applying a vector-to-vector…
This research was devoted to investigate the inverse spectral problem of Sturm-Liouville operator with many frozen arguments. Under some assumptions, the authors obtained uniqueness theorems. At the end, a numerical simulation for the…