Approximation on the complex sphere
  We develop new elements of harmonic analysis on the complex sphere on the basis of which Bernstein's, Jackson's and Kolmogorov's inequalities are established. We apply these results to get order sharp estimates of $m$-term approximations. The results obtained is a synthesis of new results on classical orthogonal polynomials, harmonic analysis on manifolds and geometric properties of Euclidean spaces. 
Huda Alsaud, Alexander Kushpel and Jeremy Levesley
math.CA