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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1972, Volume 11, Issue 5, Pages 559–567 (Mi mz9823)

On a transformation operator for a system of Sturm–Liouville equations

M. B. Velieva, M. G. Gasymovb

a Institute of Mathematics and Mechanics, Academy of Sciences of the Azerbaidzhan SSR
b S. M. Kirov Azerbaidzhan State University

Abstract: We prove the existence of a transformation operator with a condition at infinity that sends a solution of the matrix equation $-y"+My=\lambda^2y$ ($M$ is a constant Hermitian matrix) into a solution of the matrix equation $-y"+Q(x)y+My=\lambda^2y$ (the matrix function $Q(x)$ is continuously differentiable for $0\leqslant x<\infty$ and it is Hermitian for each $x$ belonging to $[0,\infty)$); we study some properties of the kernel of the transformation operator.

Full text: PDF file (783 kB)

English version:
Mathematical Notes, 1972, 11:5, 341–346

Bibliographic databases:

UDC: 517.9

Citation: M. B. Veliev, M. G. Gasymov, “On a transformation operator for a system of Sturm–Liouville equations”, Mat. Zametki, 11:5 (1972), 559–567; Math. Notes, 11:5 (1972), 341–346

Citation in format AMSBIB
\Bibitem{VelGas72} \by M.~B.~Veliev, M.~G.~Gasymov \paper On a transformation operator for a system of Sturm--Liouville equations \jour Mat. Zametki \yr 1972 \vol 11 \issue 5 \pages 559--567 \mathnet{http://mi.mathnet.ru/mz9823} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=308508} \zmath{https://zbmath.org/?q=an:0273.34013|0265.34030} \transl \jour Math. Notes \yr 1972 \vol 11 \issue 5 \pages 341--346 \crossref{https://doi.org/10.1007/BF01158649}