Contrast with the Hille-Yosida's Theorem and the Strongly Continuous Semigroup of Contraction for a Third-order Differential Operator

Abstract

In this work, we prove that the closed right half-plane is contained in the resolvent set of odd-order differential operator A and that the norm of the resolvent operator of A on z with positive real part is bounded by the inverse of the real part of z, which connects us to the Hille-Yosida’s Theorem. Furthermore, we explore the connection between being a strongly continuous semigroup of contraction and the dissipativeness of its infinitesimal generator. Finally, we generalize the results obtained for odd-order differential operators.