The d

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• 作者：Yuk J. Leung ; Wenbo V. Li ; Rakesh
• 关键词：Polarization constant ; Product of linear functionals
• 刊名：Journal of Functional Analysis
• 出版年：2008
• 出版时间：15 November 2008
• 年：2008
• 卷：255
• 期：10
• 页码：2861-2871
• 全文大小：172 K

文摘

In [C. Benítez, Y. Sarantopoulos, A. Tonge, Lower bounds for norms of products of polynomials, Math. Proc. Cambridge Philos. Soc. 124 (3) (1998) 395–408] it was conjectured that for all unit vectors u₁,…,u_d in , with equality occurring iff u₁,…,u_d are orthonormal. We relate this to a conjecture about solutions of Ay=y⁻¹, where A=(u_i,u_j), and show that if the conjecture fails then the u₁,…,u_d minimizing must be linearly dependent. We also show for certain families of u₁,…,u_d.