(untitled) (Международный научный журнал «Инженер», 2026)
This work studies the geometric properties of eigenfunctions of fractional powers of the self-adjoint Laplace operator. The sturucture of nodal domains bounded by nodal surfaces, on which the eigenfunction vanishes, is investigated. The behavior of these nodal domains is analyzed depending on the eigenvalue. The paper derives estimates showing that the width of the nodal domain decreases as the eigenvalue increases. From these estimates, it follows that the width of the nodal domain tends to zero as the eigenvalue increases.