Year-end Sale % OFF 
Abstract
We study spectral multipliers of right invariant sub-Laplacians with drift Open image in new window on a connected Lie group G. The operators we consider are self-adjoint with respect to a positive measure Open image in new window , whose density with respect to the left Haar measure λ G is a nontrivial positive character Open image in new window of G. We show that if p≠2 and G is amenable, then every Open image in new window spectral multiplier of Open image in new window extends to a bounded holomorphic function on a parabolic region in the complex plane, which depends on p and on the drift. When G is of polynomial growth we show that this necessary condition is nearly sufficient, by proving that bounded holomorphic functions on the appropriate parabolic region which satisfy mild regularity conditions on its boundary are Open image in new window spectral multipliers of Open image in new window .
Published Version
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.
