This is a preview of subscription content, log in via an institution to check access.
Literature cited
I. C. Gohberg and M. G. Krein, Introduction to the Theory of Linear Non-self-Adjoint Operators, Amer. Math. Soc., Providence (1969).
Yu. I. Lyubich and V. A. Tkachenko, “Theory and certain applications of the local Laplace transform,” Mat. Sb.,70 (112), No. 3, 416–437 (1966).
V. B. Lidskii, “On the summability of series in terms of the principal vectors of nonself-adjoint operators,” Trudy Moskov. Mat. Obshch.,11, 3–35 (1962).
A. G. Rutkas, “The Cauchy problem for the equation Ax'(t) + Bx(t) = f(t),”Differents. Uravn.,11, No. 11, 1996–2010 (1975).
N. I. Radbel', Ordered Pairs of Linear Operators and the Cauchy Problem for the Equation Ax'(t) + Bx(t) = 0 in a Banach Space. Candidate's Dissertation, Donetsk (1984).
L. A. Vlasenko and A. G. Rutkas, The Investigation of the Equation Ax'(t) + Bx(t) = f(t) with the Aid of the Resolvent of the Pencil λA + B. Manuscript deposited at VINITI, No. 4885-82 (1982).
Additional information
Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 48, pp. 46–51, 1987.
Rights and permissions
About this article
Cite this article
Vlasenko, L.A. On the completeness of the normal solutions of the equation Au′(t) + Bu(t) = f(t). J Math Sci 49, 883–886 (1990). https://doi.org/10.1007/BF02205633
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02205633