On the convergence in W 2 m of spectral expansions for a spectral problem with boundary conditions of the third kind one of which contains the spectral parameter

We consider a spectral problem with boundary conditions of the third kind one of which contains the spectral parameter occurring linearly. We study the basis property of the system of eigenfunctions of this spectral problem in W ₂ ^m . We obtain conditions under which the system becomes a basis in this space after the deletion of any single eigenfunction.