Contrast with the Hille-Yosida's Theorem and the Strongly Continuous Semigroup of Contraction for a Third-order Differential Operator
DOI:
https://doi.org/10.14738/ejas.1403.2378Keywords:
Semigroup of contraction, Hille-Yosida’s Theorem, third-order differential operator, dissipative operator, Periodic Sobolev spaces, Fourier TheoryAbstract
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.
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