希尔伯特不等式中的最佳常数

IF 0.8 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae Pub Date : 2023-12-02 DOI:10.1016/j.exmath.2023.125530

Ole Fredrik Brevig

引用次数: 1

摘要

建立∑m=1∞∑n=1∞aman¯mn(max(m,n))3≤43∑m=1∞|am|2对复数a=(a1,a2，…)的每一个平方可和数列都成立，并且常数4/3不能被任何更小的数代替。我们的证明植根于1911年一篇关于舒尔的双线性形式的开创性论文，出于解释性的原因，我们包括了对他的方法的阐述。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The best constant in a Hilbert-type inequality

We establish that $\sum_{m = 1}^{\infty} \sum_{n = 1}^{\infty} a_{m} \bar{a_{n}} \frac{m n}{{(max (m, n))}^{3}} \leq \frac{4}{3} \sum_{m = 1}^{\infty} {| a_{m} |}^{2}$ holds for every square-summable sequence of complex numbers $a = (a_{1}, a_{2}, \dots)$ and that the constant $4 / 3$ cannot be replaced by any smaller number. Our proof is rooted in a seminal 1911 paper concerning bilinear forms due to Schur, and we include for expositional reasons an elaboration on his approach.

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来源期刊

Expositiones Mathematicae 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

40 days

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