in this manuscript, we study the inverse problem for non self-adjoint sturm--liouville operator $-d^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. by defining  a new hilbert space and  using its spectral data of a kind, it is shown that the potential function can be uniquely determined by part of a set of values of eigenfunctions at som...

Abstract We study a Miura-type transformation between Kac - van Moerbeke (Volterra) and Toda lattices in terms of the inverse spectral problem for Jacobi operators, which appear Lax representation such systems. This method, amounts to reconstruction operator from moments its Weyl function, can be used solving initial-boundary value both It is shown that Miura easily described these moments. Usi...

Assume that $M$ is a compact Riemannian manifold of bounded geometry given by restrictions on its diameter, Ricci curvature and injectivity radius. we are given, with some error, the first eigenvalues Laplacian $\Delta_g$ as well corresponding eigenfunctions restricted an open set in $M$. We then construct stable approximation to $(M,g)$. Namely, metric space which differ, proper sense, just li...

This paper is concerned with the inverse spectral problem for third-order differential equation distribution coefficient. The consists in recovery of expression coefficients from data two boundary value problems separated conditions. For this problem, we solve most fundamental question theory about necessary and sufficient conditions solvability. In addition, prove local solvability stability p...

We analyze an inverse problem associated with the time-harmonic Rayleigh system on a flat elastic half-space concerning recovery of Lamé parameters in slab beneath traction-free surface. employ Markushevich substitution, while data are captured Jost function, and we point out parallels corresponding for Schrödinger equation. The function can be identified spectral data. derive Gel’fand-Levitan ...

We establish that the potential appearing in a fractional Schrödinger operator is uniquely determined by an internal spectral data.