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<p>Selfadjoint and maximal dissipative extensions of a non-densely defined symmetric operator <i>S</i> in an infinite-dimensional separable Hilbert space are considered and their compressions on the subspace <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="20_2024_2792_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="50" /> </InlineMediaObject> <EquationSource Format="TEX">\({\overline{dom}\,} S\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mover> <mrow> <mi mathvariant="italic">dom</mi> </mrow> <mo>¯</mo> </mover> <mspace width="0.166667em" /> </mrow> <mi>S</mi> </mrow> </math></EquationSource> </InlineEquation> are studied. The main focus is on the case <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="20_2024_2792_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="133" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathrm{codim\,}{\overline{dom}\,}S=\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mi mathvariant="normal">codim</mi> <mspace width="0.166667em" /> </mrow> <mrow> <mover> <mrow> <mi mathvariant="italic">dom</mi> </mrow> <mo>¯</mo> </mover> <mspace width="0.166667em" /> </mrow> <mi>S</mi> <mo>=</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation>. New properties of the characteristic functions of non-densely defined symmetric operators are established.</p>

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Compressions of Selfadjoint and Maximal Dissipative Extensions of Non-densely Defined Symmetric Operators

  • 期刊论文

  • 发表日期：

    2025年1月11日

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  • Y. M. Arlinskiĭ

摘要

Selfadjoint and maximal dissipative extensions of a non-densely defined symmetric operator S in an infinite-dimensional separable Hilbert space are considered and their compressions on the subspace \({\overline{dom}\,} S\) dom ¯ S are studied. The main focus is on the case \(\mathrm{codim\,}{\overline{dom}\,}S=\infty \) codim dom ¯ S = ∞ . New properties of the characteristic functions of non-densely defined symmetric operators are established.