What question did this study set out to answer?

To determine sharp upper bounds for fractional powers of linear operators related to higher-order equations.

January 21, 2026Bulletin of the London Mathematical Society0 citationsOpen Access

The sharp upper bound for generation of linear semigroups by higher order equations with fractional powers

FBFlank D. M. BezerraUniversidade Federal da Paraíba LSLucas A. SantosInstituto Federal de Educação Ciência e Tecnologia da Paraíba MSMaria J. M. SilvaUniversidade Federal da Paraíba

Key Points

To determine sharp upper bounds for fractional powers of linear operators related to higher-order equations.
Analyzed higher-order equations in the context of Hilbert spaces.
Investigated the properties of unbounded linear operators.
Derived mathematical proofs to establish upper bounds.
Found a sharp upper bound for fractional powers of linear operators.
Demonstrated implications for the theory of linear semigroups in mathematics.

Abstract

Abstract In this paper, we consider a class of higher‐order equations and show a sharp upper bound on fractional powers of unbounded linear operators associated with higher‐order abstract equations in Hilbert spaces.

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