Abstract
Let V and W be any convex and origin-symmetric bodies in Rn . Assume that for some A ∈LRn→Rn, detA≠0, V is contained in the ellipsoid A−1B2n, where B2n is the unit Euclidean ball. We give a lower bound for the W-radius of sections of A−1V in terms of the spectral radius of A∗A and the expectations of ‖⋅‖V and ‖⋅‖Wo with respect to Haar measure on Sn−1⊂Rn. It is shown that the respective expectations are bounded as n→∞ in many important cases. As an application we offer a new method of evaluation of n-widths of multiplier operators. As an example we establish sharp orders of n-widths of multiplier operators Λ:LpMd→LqMd, 1<q≤2≤p<∞ on compact homogeneous Riemannian manifolds Md. Also, we apply these results to prove the existence of flat polynomials on Md.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.