It is known that the Green function of a boundary value problem is a meromorphic function of a spectral parameter. When the boundary conditions contain integro-differential terms, then the meromorphism of the Green's function of such a problem can also be proved. In this case, it is possible to write out the structure of the residue at the singular points of the Green's function of the boundary value problem with integro-differential perturbations. An analysis of the structure of the residue allows us to state that the corresponding functions of the original operator are sufficiently smooth functions. Surprisingly, the adjoint operator can have non-smooth eigenfunctions. The degree of non-smoothness of the eigenfunction of the adjoint operator to an operator with integro-differential boundary conditions is clarified. It is indicated that even those conjugations to multipoint boundary value problems have non-smooth eigenfunctions.
boundary conditions, Green's function Operator, strongly regular boundary conditions, Riesz basis, asymptotics, Resolution, boundary functions, simple zero, adjoint operator
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