Kushpel, AlexanderTaş, KenanKushpel, AlexanderTas, KenanMatematik2020-12-242020-12-242021Kushpel, A.; Taş, Kenan (2021). "The radii of sections of origin-symmetric convex bodies and their applications", Journal of Complexity, Vol. 62.0885-064X1090-2708https://doi.org/10.1016/j.jco.2020.101504Kushpel, Alexander/0000-0002-9585-744XLet V and W be any convex and origin-symmetric bodies in R-n . Assume that for some A is an element of L (R-n -> R-n), det A not equal 0, V is contained in the ellipsoid A(-1)B((2))(n), where B-(2)(n) is the unit Euclidean ball. We give a lower bound for the W-radius of sections of A(-1) V in terms of the spectral radius of AA and the expectations of parallel to . parallel to(V) and parallel to . parallel to(W)0 with respect to Haar measure on Sn-1 subset of R-n. It is shown that the respective expectations are bounded as n -> infinity 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 Lambda : L-p (M-d) -> L-q (M-d), 1 < q <= 2 <= p < infinity on compact homogeneous Riemannian manifolds M-d. Also, we apply these results to prove the existence of flat polynomials on M-d. (c) 2020 Elsevier Inc. All rights reserved.eninfo:eu-repo/semantics/openAccessConvex BodyVolumeMultiplierWidthArticle6210.1016/j.jco.2020.1015042-s2.0-85087814993WOS:000591354500002Q1Q2