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Differential Equations, Vol. 41, No. 6, 2005, pp. 818–823. Translated from Differentsial'nye Uravneniya, Vol. 41, No. 6, 2005, pp. 781–786. Original Russian Text Copyright c 2005 by Yurko. ORDINARY DIFFERENTIAL EQUATIONS An Inverse Problem for Di erential Systems on a Finite Interval in the Case of Multiple Roots of the Characteristic Polynomial V. A. Yurko Saratov State University Received March 24, 2004 1. We consider the following system of di erential equations on a nite interval: Y (x)+ B(x)Y (x)= %B Y (x); 0 <x<T: (1) Here Y =[y ] is a column vector (t stands for transposition), % is the spectral parameter, k=1;:::;n B is a constant diagonal matrix with distinct complex numbers 6=0, i =1;:::;p, of multiplicities n (p> 1;n + + n = n) on the main diagonal, and i 1 p B(x)=[B (x)] ; k k;=1;:::;n where B (x) 2 L(0;T ) are complex-valued functions. The matrix B(x) is called the potential. In this paper, we study the inverse spectral problem for system (1) with arbitrary complex and with arbitrary behavior of the spectrum. As the main spectral characteristic, we introduce and investigate the so-called Weyl matrix, which is an analog of the classical Weyl
Differential Equations – Springer Journals
Published: Jul 27, 2005
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