Approximation on the complex sphere

Abstract

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.

References in corpus (3)

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• Extending the range of error estimates for radial approximation in Euclidean space and on spheres
• A Multiplier Version of the Bernstein Inequality on the Complex Sphere