Open Access

# Boundary triples for integral systems on the half-line

### Abstract

Let $P$, $Q$ and $W$ be real functions of locally bounded variation on $[0,\infty)$ and let $W$ be non-decreasing. In the case of absolutely continuous functions $P$, $Q$ and $W$ the following Sturm-Liouville type integral system: $$\label{eq:abs:is} J\vec{f}(x)-J\vec{a} = \int_0^x \begin{pmatrix}\lambda dW-dQ & 0\\0 & dP\end{pmatrix} \vec{f}(t), \quad J = \begin{pmatrix}0 & -1\\1 & 0\end{pmatrix}$$ (see [5]) is a special case of so-called canonical differential system (see [16, 20, 24]). In [27] a maximal $A_{\max}$ and a minimal $A_{\min}$ linear relations associated with system (1) have been studied on a compact interval. This paper is a continuation of [27] , it focuses on a study of $A_{\max}$ and $A_{\min}$ on the half-line. Boundary triples for $A_{\max}$ on $[0,\infty)$ are constructed and the corresponding Weyl functions are calculated in both limit point and limit circle cases at $\infty$.

Key words: Integral system, boundary triple, symmetric linear relation, Weyl circles.

### Article Information

 Title Boundary triples for integral systems on the half-line Source Methods Funct. Anal. Topology, Vol. 25 (2019), no. 1, 84-96 MathSciNet MR3935582 Milestones Received 09/08/2018; Revised 25/01/2019 Copyright The Author(s) 2019 (CC BY-SA)

### Authors Information

D. Strelnikov
Vasyl’ Stus Donetsk National University

### Citation Example

D. Strelnikov, Boundary triples for integral systems on the half-line, Methods Funct. Anal. Topology 25 (2019), no. 1, 84-96.

### BibTex

@article {MFAT1143,
AUTHOR = {D. Strelnikov},
TITLE = {Boundary triples for integral systems on the half-line},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {25},
YEAR = {2019},
NUMBER = {1},
PAGES = {84-96},
ISSN = {1029-3531},
MRNUMBER = {MR3935582},
URL = {http://mfat.imath.kiev.ua/article/?id=1143},
}

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