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Boundary triples for integral systems on finite intervals

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Abstract

Let P, Q, and W be real functions of bounded variation on [0, l], and let W be nondecreasing. The integral system

$$ J\overrightarrow{f}(x)-J\overrightarrow{a}=\underset{0}{\overset{x}{\int }}\left(\begin{array}{cc}\uplambda dW- dQ& 0\\ {}0& dP\end{array}\right)\overrightarrow{f}(t),\kern1em J=\left(\begin{array}{cc}0& -1\\ {}1& 0\end{array}\right) $$
(0.1)

on a finite compact interval [0, l] was considered in [6]. The maximal and minimal linear relations A max and A min associated with the integral system (0.1) are studied in the Hilbert space L2(W). It is shown that the linear relation A min is symmetric with deficiency indices n ± (A min ) = 2 and A max = \( {A}_{min}^{\ast }. \) Boundary triples for A max are constructed, and the the corresponding Weyl functions are calculated.

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Correspondence to Dmytro Strelnikov.

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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 14, No. 3, pp. 418–439 July–September, 2017.

The author is grateful to Professor V. Derkach for his constant attention to this work.

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Strelnikov, D. Boundary triples for integral systems on finite intervals. J Math Sci 231, 83–100 (2018). https://doi.org/10.1007/s10958-018-3807-z

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