On generalized resolvents and spectral functions of differential operators of even order in a space of vector-valued functions

We consider a self-adjoint differential expression of even order in a space of vector-valued functions. We prove that an arbitrary generalized resolvent of the minimal operator $L_0$ induced by this differential expression is an integral operator and we derive a formula for all of the spectral functions (orthogonal and nonorthogonal) of the operator $L_0$.