<p>In this paper we consider a two–dimensional Hamiltonian integral system on an interval <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$[ a,b )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">[</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. We investigate the definiteness and surjectivity properties and define associated with this system the maximal <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$S_{\max }$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>S</mi> <mo movablelimits="true">max</mo> </msub> </math></EquationSource> </InlineEquation> and minimal <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$S_{\min }$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>S</mi> <mo movablelimits="true">min</mo> </msub> </math></EquationSource> </InlineEquation> linear relations. For an improper gauge <InlineEquation ID="IEq7"> <EquationSource Format="TEX">${\mathfrak L}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="fraktur">L</mi> </math></EquationSource> </InlineEquation>, we calculate the <InlineEquation ID="IEq8"> <EquationSource Format="TEX">${\mathfrak L}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="fraktur">L</mi> </math></EquationSource> </InlineEquation>-resolvent matrix and describe the set of <InlineEquation ID="IEq9"> <EquationSource Format="TEX">${\mathfrak L}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="fraktur">L</mi> </math></EquationSource> </InlineEquation>-resolvents of the linear relation <InlineEquation ID="IEq10"> <EquationSource Format="TEX">$S_{\min }$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>S</mi> <mo movablelimits="true">min</mo> </msub> </math></EquationSource> </InlineEquation> in the cases when the system is either quasiregular, limit circle, or limit point at <i>b</i>.</p>

${\mathfrak L}$-Resolvent Matrices for Hamiltonian Integral Systems

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2026年3月1日

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Volodymyr Derkach,
Dmytro Strelnikov

摘要

In this paper we consider a two–dimensional Hamiltonian integral system on an interval $[ a,b )$ $[a, b)$ . We investigate the definiteness and surjectivity properties and define associated with this system the maximal $S_{\max }$ $S_{max}$ and minimal $S_{\min }$ $S_{min}$ linear relations. For an improper gauge ${\mathfrak L}$ $L$ , we calculate the ${\mathfrak L}$ $L$ -resolvent matrix and describe the set of ${\mathfrak L}$ $L$ -resolvents of the linear relation $S_{\min }$ $S_{min}$ in the cases when the system is either quasiregular, limit circle, or limit point at b.

\({\mathfrak L}\)-Resolvent Matrices for Hamiltonian Integral Systems

摘要