Publication Date:
2015-09-19
Description:
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 $A^k$ of a positive holomorphic line bundle on a compact Kähler manifold with cardinality bigger than $1-\varepsilon $ times the dimension of the space of global holomorphic sections to $A^k$ .
Print ISSN:
0024-6093
Electronic ISSN:
1469-2120
Topics:
Mathematics
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