Estimates for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e46" altimg="si25.svg"><mml:mi>n</mml:mi></mml:math>-widths of sets of smooth functions on complex spheres

In this work we investigate n-widths of multiplier operators Λ∗ and Λ, defined for functions on the complex sphere Ωd ℂd, associated with sequences multipliers type {λm,n∗}m,n∈N, λm,n∗=λ(m+n) {λm,n}m,n∈N, λm,n=λ(max{m,n}), respectively, a bounded function λ [0,∞). If Λ are from Lp(Ωd) into Lq(Ωd), 1≤p,q≤∞, Up is closed unit ball Lp(Ωd), study lower upper estimates Kolmogorov, linear, Gelfand Bernstein, sets Λ∗Up ΛUp in Lq(Ωd). As application obtain, particular, Kolmogorov n-width classes Sobolev, finitely differentiable, infinitely differentiable analytic sphere, which order sharp various important situations.