Abstract
Let L be a sub-Laplacian on a connected Lie group G of polynomial growth. It is well known that, if F:R→C is in the Schwartz class S(R), then the convolution kernel KF(L) of the operator F(L) is in the Schwartz class S(G). Here we prove a sort of converse implication for a class of groups G including all solvable noncompact groups of polynomial growth. We also discuss the problem whether integrability of KF(L) implies continuity of F.
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.
