Related papers: Periodic and almost periodic potentials in the inv…
We consider two phaseless inverse problems for elliptic equation. The statements of these problems differ from have considered. Namely, instead of given information about modulus of scattering waves, we consider the information related to…
In this paper, we study the direct and inverse spectral problems for the Schrodinger operator with two generalized Regge boundary conditions. For the direct problem, we give the properties of the spectrum, including the asymptotic…
We suggest a new statement of the inverse spectral problem for Sturm--Liouville-type operators with constant delay. This inverse problem consists in recovering the coefficient (often referred to as potential) of the delayed term in the…
We show the existence of periodic solutions for continuous symmetric perturbations of certain planar power law problems.
New inverse and half-inverse problems: {\it sliding problems} are introduced. In this way several physically important equations are recovered from the quantum defect. In particular, sliding problems are solved for radial Schr\"odinger…
Consider the problem of scattering of electromagnetic waves by a doubly periodic structure. The medium above the structure is assumed to be inhomogeneous characterized completely by an index of refraction. Below the structure is a perfect…
In general case of deformed Heisenberg algebra leading to the minimal length we present a definition of the square inverse position operator. Our proposal is based on the functional analysis of the square position operator. Using this…
We discuss, in the context of inverse linear problems in Hilbert space, the notion of the associated infinite-dimensional Krylov subspace and we produce necessary and sufficient conditions for the Krylov-solvability of a given inverse…
The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we…
These lecture notes evolve around mathematical concepts arising in inverse problems. We start by introducing inverse problems through examples such as differentiation, deconvolution, computed tomography and phase retrieval. This then leads…
In this study, the theorem on necessary and sufficient conditions for the solvability of inverse problem for Sturm-Liouville operator with discontinuous coefficient is proved and the algorithm of reconstruction of potential from spectral…
We consider a generalization of the three spectral inverse problem, that is, for given spectrum of the Dirichlet-Dirichlet problem (the Sturm-Liouville problem with Dirichlet conditions at both ends) on the whole interval $[0,a]$, parts of…
This paper is concerned with the inverse spectral problem for the third-order differential equation with distribution coefficient. The inverse problem consists in the recovery of the differential expression coefficients from the spectral…
Direct and inverse scattering problems for a third-order self-adjoint differential operator on the whole axis are studied. This operator is the sum of three summands: operator of third derivative, operator of multiplication by a function,…
We relax the regularity condition on potentials of the Schr\"odinger equation in uniqueness results on the inverse boundary value problem which were recently proved in [11] and [5].
In this paper, we study the semilinear wave equations with the inverse-square potential. By transferring the original equation to a "fractional dimensional" wave equation and analyzing the properties of its fundamental solution, we…
We present n-dimensional vortex-ring-like and potential-like solutions with unusual properties related to some elliptical differential equations with compact sources. Solutions have almost 3- or 2-dimensional behaviour in the spaces with…
The Schroedinger equation is considered on the line when the potential is real valued, compactly supported, and square integrable. The nonuniqueness is analyzed in the recovery of such a potential from the data consisting of the ratio of a…
We discuss some aspects of Extrapolation theory. The presentation includes many examples and open problems.
In the present paper we describe a method for solving inverse problems for the Helmholtz equation in radially-symmetric domains given multi-frequency data. Our approach is based on the construction of suitable trace formulas which relate…