turkmath.org

In this talk an inverse spectral problem is considered with respect to the domain for the Schrödinger equation. Using the introduced space of the pairs of the convex domains a new definition of the domain variation is given. The first variation of the eigenvalues with respect to domain is calculated, a new formula for the eigenvalues of the Schrödinger operator is proved. A definition of s-function is introduced and a scheme is proposed to reconstruct the domain by the given set of the s-functions. Some particular cases are also considered.