Related papers: Solution of the inverse spectral problem for a con…
We prove the long standing conjecture in the theory of two-point boundary value problems that completeness and Dunford's spectrality imply Birkhoff regularity. In addition we establish the even order part of S.G.Krein's conjecture that…
In recent years, there appeared a considerable interest in the inverse spectral theory for functional-differential operators with constant delay. In particular, it is well known that specification of the spectra of two operators $\ell_j,$…
This paper deals with differential pencils possessing a term depending on the unknown function with a fixed argument. We deduce the so called main equation together with its fine structure for the spectral problem. Then, according to the…
In recent years, there appeared a considerable interest in the inverse spectral theory for functional-differential operators with constant delay. In particular, it is well known that, for each fixed $\nu\in\{0,1\},$ the spectra of two…
This paper addresses the inverse obstacle scattering problem of simultaneously reconstructing the obstacle geometry and boundary conditions from multi-frequency near-field backscattering data. We first establish rigorous high-frequency…
Inverse scattering problem for an operator, which is a sum of the operator of the third derivative and of an operator of multiplication by a real function, is solved. The main closed system of equations of inverse problem is obtained. This…
In this paper the asymptotic distributions are exactly solved for linearly independent solutions considering problems of the second order and for the coefficients of asymptotic destribution the recurent formulas are obtained. Further, using…
We study Sturm-Liouville operators on closed sets of a special structure, which are sometimes referred as time scales and often appear in modelling various real processes. Depending on the set structure, such operators unify both…
The inverse spectral theory for a self-adjoint one-dimensional Dirac operator associated periodic potentials is formulated via a Riemann-Hilbert problem approach. The resulting formalism is also used to solve the initial value problem for…
In this paper we study an inverse boundary value problem for Maxwell's equations. The goal is to reconstruct perturbations in the refractive index of the medium inside an object from the knowledge of the tangential trace of an electric…
The boundary-value problem on semi-axis for one class operator-differential equations of the fourth order, the main part of which has the multiple characteristic is investigated in this paper in Sobolev type weighted space. Correctness and…
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…
We introduce Robin boundary conditions for biharmonic operators, which are a model for elastically supported plates and are closely related to the study of spaces of traces of Sobolev functions. We study the dependence of the operator, its…
In this paper we consider a twofold Ellis-Gohberg type inverse problem in an abstract *-algebraic setting. Under natural assumptions, necessary and sufficient conditions for the existence of a solution are obtained, and it is shown that in…
We formulate the inverse spectral theory for a non-self-adjoint one-dimensional Dirac operator associated periodic potentials via a Riemann-Hilbert problem approach. We use the resulting formalism to solve the initial value problem for the…
In this paper, we explore the inverse spectral problem of Sturm-Liouville operator on a star-like graph. To this fixed star-like graph centered at the origin as its vertex, we attach $m$ edges. On each edge, we impose the Sturm-Liouville…
In this paper, a Sturm-Liouville boundary value problem equiped with conformable fractional derivates is considered. We give some uniqueness theorems for the solutions of inverse problems according to the Weyl function, two given spectra…
In this paper, we consider an inverse problem to determine a semilinear term of a parabolic equation from a single boundary measurement of Neumann type. For this problem, a reconstruction algorithm is established by the spectral…
The inverse spectral problem is investigated for the matrix Sturm-Liouville equation on a finite interval. Properties of spectral characteristics are provided, a constructive procedure for the solution of the inverse problem along with…
We consider a boundary-value problem for the second order elliptic differential operator with rapidly oscillating coefficients in a domain $\Omega_{\epsilon}$ that is $\epsilon-$periodically perforated by small holes. The holes are divided…