Abstract
We consider two infinitesimal generators A, B of strongly continuous groups in a general Banach space X, such that either the commutator between A and B commutes both with e tA and with e tB , or the commutator is a multiple of A. We prove that under suitable assumptions the sum A+ B and the commutator [ A, B] are closable, and their closures generate strongly continuous groups. We give explicit representation formulas for such groups, in terms of e tA and e tB .
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
