Minimal projections onto spaces of polynomials on real euclidean spheres

Abstract

Este documento es la versión aceptada del artículo "Minimal projections onto spaces of polynomials on real Euclidean spheres" publicado en el Journal of the London Mathematical Society, 113(1)We investigate projection constants within classes of multivariate polynomials over finitedimensional 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 L1-norms of specific Jacobi polynomials. As a consequence, we present exact formulas, computable expressions and asymptotically accurate estimates for them.Defant, A., Galicer, D., Mansilla, M., Mastyło, M., & Muro, S. (2026). Minimal projections onto spaces of polynomials on real Euclidean spheres. Journal of the London Mathematical Society, 113(1). Portico. https://doi.org/10.1112/jlms.7042