On a spectral problem in the plane angle for second order singular differential operator

In this paper the spectral problem of a special form for the singular elliptic operator of the second order in an unbounded angular sector on a plane is solved. The rearrangement of eigenvalues and changing the shape of eigenfunctions with variations in the sector angle is shown. The necessity of changing the boundary conditions during the transformation of the solution search area from an angular sector to a half-plane is established.