Completeness of a system of root functions of a nonlocal problem in \(L_ p\).
This paper is devoted to the properties of expansions in the root functions of nonlocal elliptic problems. To this end the author introduces operators acting on the Sobolev spaces \(W^s_q(\Omega)\) and shows that under certain assumptions, all these operators have the same root function systems. Thus he gives sufficient conditions for the completeness of the root function system for nonlocal elliptic problems in the Sobolev spaces \(W^\ell_p(Q)\).
scientific article; zbMATH DE number 1928225