Regular spectral problems in vector-function spaces (Q1112223)

We consider in a space of vector-functions the spectral problem \[ \ell (y,\lambda)=y^{(n)}+P_ 1(x,\lambda)y^{(n-1)}+...+P_ n(x,\lambda)y=0, \] \[ U_{\nu}(y)=\sum^{k_{\nu}}_{j=1}A_{\nu j}y^{(j)}(0)+B_{\nu j}y^{(j)}(1)=0,\quad \nu =1,2,...,n, \] where \(y(x)=(y_ 1(x),...,y_ m(x))\); \(P_ s(x,\lambda)=\lambda^ sQ_{ss}+\sum^{s-1}_{j=1}\lambda^ jP_{sj}(x)\) are matrices \(m\times m\); \(A_{\nu j},B_{\nu j},Q_{ss}\) are constant matrices, det \(Q_{nn}\neq 0\). The boundary conditions are assumed to be normed.