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The deficiency indices of a system of first-order differential equations. (English. Russian original) Zbl 0942.34071

Sib. Math. J. 38, No. 6, 1182-1183 (1997); translation from Sib. Mat. Zh. 38, No. 6, 1360-1361 (1997).
The theorem by B. M. Levitan on the deficiency indices of Dirac-type systems is extended to systems of the form \[ \frac{dw}{dx} = i z J H (x) w, \qquad 0 \leq x \leq \infty. \] Here, \(H(x)\geq 0\) is a locally summable matrix-valued function of order \(2m \times 2m\), \[ J=\begin{pmatrix} 0 & E_m \\ E_m & 0 \end{pmatrix}. \]

MSC:

34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
34L05 General spectral theory of ordinary differential operators
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References:

[1] L. A. Sakhnovich, ”Problems of factorization and operator identities,” Uspekhi Mat. Nauk,41, No. 1, 3–55 (1986). · Zbl 0613.47017
[2] B. M. Levitan and I. S. Sargsyan, Introduction to Spectral Theory [in Russian], Nauka, Moscow (1970). · Zbl 0225.47019
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