The Adjoint of α -Times-Integrated C -Regularized Semigroups

Mostafa Bachar ()
Additional contact information
Mostafa Bachar: Department of Mathematics, College of Sciences, King Saud University, Riyadh 11451, Saudi Arabia

Mathematics, 2024, vol. 12, issue 10, 1-11

Abstract: We consider an operator { S ( t ) } t ≥ 0 on a Banach space X with generator A , characterized by being an α -times-integrated C -regularized semigroup. The adjoint family S * ( t ) : X * → X * is introduced for analysis. { S * ( t ) } t ≥ 0 maintains the characteristics of an α -times-integrated C -regularized semigroup, though with strong continuity and Bochner integrals being substituted by weak* continuity and weak* integrals, respectively. Our investigation focuses on the closed subspace X ⊙ , where { S * ( t ) } t ≥ 0 exhibits strong continuity. Additionally, a comparison between the adjoint A * of A and the generator of the adjoint family is conducted.

Keywords: ? -times-integrated C -regularized semigroup; adjoint of ? -times-integrated C -regularized semigroup; semigroup generator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/10/1561/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/10/1561/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:10:p:1561-:d:1396262

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().