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<p>In this paper we consider a non-integer (fractional)-order nonselfadjoint boundary-value problem so that the fractional-order equation is a kind of left-definite equation. We construct a dissipative operator in a Sobolev space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(H^{1}(a,b)\)</EquationSource> </InlineEquation> and we introduce several results on the spectral properties of the related operators. In particular, we construct an inverse operator with the aid of the Dirac-delta function and we apply Krein’s theorem to the inverse operator which is compact having a nuclear imaginary component.</p>

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A left-definite non-integer-order dissipative operator

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  • 发表日期：

    2026年5月8日

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摘要

In this paper we consider a non-integer (fractional)-order nonselfadjoint boundary-value problem so that the fractional-order equation is a kind of left-definite equation. We construct a dissipative operator in a Sobolev space \(H^{1}(a,b)\) and we introduce several results on the spectral properties of the related operators. In particular, we construct an inverse operator with the aid of the Dirac-delta function and we apply Krein’s theorem to the inverse operator which is compact having a nuclear imaginary component.