Jackson inequalities on sphere in \(L_ 2\)
[In the paper presented the authors deal with the space \(L_2(S)\), decomposable into a direct orthogonal sum of finite-dimensional, invariant with respect to the rotation group \(\text{SO}(m)\). (Each subspace is composed of restrictions to the sphere of homogeneous harmonic polynomials and is a proper subspace of the Beltrami-Laplace operator corresponding to the eigenvalue \(-i\times(i+m-1)\).) Functions belonging to \(L_2(S)\) are uniquely decomposable into mean-convergent Fourier-Laplace series by spherical harmonics. The authors study the problem on unequalities of Jackson type between best the mean-square approximation and a continuity module. Analogous results for functions smooth on a sphere are obtained.
scientific article; zbMATH DE number 898877