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

Puntos clave

• 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.