TY - JOUR AU - Geller, Daryl AU - Pesenson, Isaac Z. PY - 2014/08/12 Y2 - 2024/03/28 TI - Kolmogorov and Linear Widths of Balls in Sobolev Spaces on Compact Manifolds JF - MATHEMATICA SCANDINAVICA JA - Math. Scand. VL - 115 IS - 1 SE - Articles DO - 10.7146/math.scand.a-18005 UR - https://www.mscand.dk/article/view/18005 SP - 96-122 AB - We determine upper asymptotic estimates of Kolmogorov and linear $n$-widths of unit balls in Sobolev norms in $L_{p}$-spaces on smooth compact Riemannian manifolds. For compact homogeneous manifolds, we establish estimates which are asymptotically exact, for the natural ranges of indices. The proofs heavily rely on our previous results such as: estimates for the near-diagonal localization of the kernels of elliptic operators, Plancherel-Polya inequalities on manifolds, cubature formulas with positive coefficients and uniform estimates on Clebsch-Gordon coefficients on general compact homogeneous manifolds. ER -