This analysis reveals the Riemann-Liouville analytic semigroup's role in Schatten and nuclear operator classes, indicating its broad implications.
In this paper, we revisit the Riemann–Liouville analytic semigroup. In particular, we completely characterize the membership in the Schatten class <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <m:msup> <m:mrow> <m:mi mathvariant="script">S</m:mi> </m:mrow> <m:mrow> <m:mi>r</m:mi> </m:mrow> </m:msup> </m:math> Sʳ on L 2 (0, 1), as well as the membership in the class of nuclear operators on L p (0, 1), p ≥ 1, and the membership in the ideal of absolutely r -summing operators for any r ≥ 1.
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Alam et al. (2026) studied this question.
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