%0 Journal Article
%T Uniformly bounded orthonormal polynomials on the sphere
%A Jordi Marzo
%A Joaquim Ortega-Cerd¨¤
%J Mathematics
%D 2014
%I arXiv
%R 10.1112/blms/bdv061
%X Given any $\varepsilon>0$, we construct an orthonormal system of $n_k$ uniformly bounded polynomials of degree at most $k$ on the unit sphere in $\mathbb R^{m+1}$ where $n_k$ is bigger than $1-\varepsilon$ times the dimension of the space of polynomials of degree at most $k$. Similarly we construct an orthonormal system of sections of powers $L^k$ of a positive holomorphic line bundle on a compact K\"ahler manifold with cardinality bigger than $1-\varepsilon$ times the dimension of the space of global holomorphic sections to $L^k$.
%U http://arxiv.org/abs/1405.5417v2