CONTRAST WITH THE HILLE-YOSIDA'S THEOREM AND THE CONTRACTION SEMIGROUP FOR AN ODD-ORDER DIFFERENTIAL OPERATOR

• DOI: 10.37572/EdArt_2706261091

• Palavras-chave: Semigroup of contraction, Hille-Yosida’s Theorem, odd-order differential operator, dissipative operator, Periodic Sobolev spaces, Fourier Theory.

• Keywords: Semigroup of contraction, Hille-Yosida’s Theorem, odd-order differential operator, dissipative operator, Periodic Sobolev spaces, Fourier Theory.

• 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 contraction semigroup and the dissipativeness of its infinitesimal generator. Finally, we generalize the results obtained.