Related papers: Inverse spectral problem for a third-order differe…
We consider the problem of variation of spectral subspaces for linear self-adjoint operators under off-diagonal perturbations. We prove a number of new optimal results on the shift of the spectrum and obtain (sharp) estimates on the norm of…
We present a technique for reconstructing a semi-infinite Jacobi operator in the limit circle case from the spectra of two different self-adjoint extensions. Moreover, we give necessary and sufficient conditions for two real sequences to be…
The spectral problem for self-adjoint extensions is studied using the machinery of boundary triplets. For a class of symmetric operators having Weyl functions of a special type we calculate explicitly the spectral projections in the form of…
This paper is related to an inverse problem for a class of Dirac operators with discontinuous coefficient and eigenvalue parameter contained in boundary conditions. The asymptotic formula of eigenvalues of this problem is examined. The…
We give a short review of results on inverse spectral problems for ordinary differential operators on a spatial networks (geometrical graphs). We pay the main attention to the most important nonlinear inverse problems of recovering…
For finite dimensional CMV matrices the mixed inverse spectral problem of reconstruction the matrix by its submatrix and a part of its spectrum is considered. A general rational interpolation problem which arises in solving the mixed…
In this study, we are concerned with spectral problems of second-order vector dynamic equations with two-point boundary value conditions and mixed derivatives, where the matrix-valued coefficient of the leading term may be singular, and the…
We discuss inverse spectral theory for singular differential operators on arbitrary intervals $(a,b) \subseteq \mathbb{R}$ associated with rather general differential expressions of the type \[\tau f = \frac{1}{r} \left(- \big(p[f' + s…
Inverse initial and inverse source problems of a time-fractional differential equation with Bessel operator are considered. Results on existence and uniqueness of solutions to these problems are presented. The solution method is based on…
The spectral properties of a class of band matrices are investigated. The reconstruction of matrices of this special class from given spectral data is also studied. Necessary and sufficient conditions for that reconstruction are found. The…
In this paper, we investigate the spectrum of the self adjoint differential operator with operator coefficitent in a separable Hilbert space. We also derive asymptotic formulas for the sum of eigenvalues of this operator.
Boundary value problems on hedgehog-type graphs for Sturm-Liouville differential operators with general matching conditions are studied. We investigate inverse spectral problems of recovering the coefficients of the differential equation…
Let $D\subset \R^n$, $n\geq 3,$ be a bounded domain with a $C^{\infty}$ boundary $S$, $L=-\nabla^2+q(x)$ be a selfadjoint operator defined in $H=L^2(D)$ by the Neumann boundary condition, $\theta(x,y,\lambda)$ be its spectral function,…
We consider an inverse spectral problem for infinite linear mass-spring systems with different configurations obtained by changing the first mass. We give results on the reconstruction of the system from the spectra of two configurations.…
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…
We study an inverse spectral problem for singular AKNS operators based on spectral data associated with two distinct values of the effective angular momentum parameter $\kappa\,$. Our main focus is the local inverse problem near the zero…
We analyze the inverse problem to reconstruct the shape of a three dimensional homogeneous dielectric obstacle from the knowledge of noisy far field data. The forward problem is solved by a system of second kind boundary integral equations.…
A complete solution to the multiplier version of the inverse problem of the calculus of variations is given for a class of hyperbolic systems of second-order partial differential equations in two independent variables. The necessary and…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
The variation of spectral subspaces for linear self-adjoint operators under an additive bounded perturbation is considered. The objective is to estimate the norm of the difference of two spectral projections associated with isolated parts…