Dzhabarzade, R. M.; Mamedova, Eh. I. On multiple completeness of eigen-elements of some two-parametric system. (Russian. English summary) Zbl 0605.47015 Izv. Akad. Nauk Az. SSR, Ser. Fiz.-Tekh. Mat. Nauk 1986, No. 2, 3-6 (1986). The authors consider the two-parametric system \((A_{0i}+\lambda A_{1i}+\lambda^ 2A_{2i}+\mu A_{3i}+\mu^ 2A_{4i})x_ i=0\), \(i=1,2\), involving bounded linear operators \(A_{ji}\) acting in separable Hilbert spaces \(H_ i\) and show that this system possesses, under additional conditions on \(A_{ji}\), a two-fold complete system of eigenvectors of the form \(x_ 1\otimes x_ 2\in H_ 1\otimes_{\alpha}H_ 2\) (\(\alpha\) being an admissible uniform cross- norm). Reviewer: J.Danesova MSC: 47A70 (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces 47A56 Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) 47A10 Spectrum, resolvent Keywords:two-parametric system; complete system of eigenvectors; admissible uniform cross-norm PDFBibTeX XMLCite \textit{R. M. Dzhabarzade} and \textit{Eh. I. Mamedova}, Izv. Akad. Nauk Az. SSR, Ser. Fiz.-Tekh. Mat. Nauk 1986, No. 2, 3--6 (1986; Zbl 0605.47015)