Minimal projections onto spaces of polynomials on real Euclidean spheres
Abstract
Abstract We investigate projection constants within classes of multivariate polynomials over finite‐dimensional real Hilbert spaces. Specifically, we consider the projection constant for spaces of spherical harmonics and spaces of homogeneous polynomials as well as for spaces of polynomials of finite degree on the unit sphere. We establish a connection between these quantities and certain weighted ‐norms of specific Jacobi polynomials. As a consequence, we present exact formulas, computable expressions, and asymptotically accurate estimates for them.
Fields of Study & Subjects
Advanced Numerical Analysis Techniques
Digital Image Processing Techniques
advanced mathematical theories
Publication details
- Journal / source
- Journal of the London Mathematical Society
- Volume
- 113
- Issue
- 1
- Publication date
- 1 January 2026
- Language
- EN