Zur Vollständigkeit des Systems der Eigenfunktionen und Hauptfunktionen irregulärer Operatorbüschel
We consider irregular eigenvalue problems of the form \[ (1)\quad \ell(y,\lambda)=\lambda^ ny+\sum^{n}_{j=1}(\sum^{j}_{k=0}p_{kj}(x)y^{(k)})\lambda^{n-j}=0,\quad(2)\quad U_{\nu}(y)=0,\quad 1\leq \nu \leq n \] with two-point boundary conditions, \(p_{jj}\in {\mathbb{C}}\) for 1\(\leq j\leq n\) and \(p_{nn}\neq 0\). We assume that all roots \(\omega_ 1,...,\omega_ n\) of the characteristic equation \(1+\sum^{n}_{j=1}p_{jj}\omega^ j=0\) are nonzero and have different arguments. If some additional conditions on (1), (2) are fulfilled, the system of all eigen- and associated functions of (1), (2) is complete in \(L_ 2[0,1]\).
scientific article; zbMATH DE number 3855794
scientific article