在最好的舒尔常数上,二次乘法数除以差分函数
Martijn Caspers1, Jesse Reimann1
1TU Delft, EWI/DIAM, P.O.Box 5031, 2600 GA Delft, The Netherlands.
Mathematische annalen
|April 7, 2025
概括
这项研究为双线舒尔乘数的边界性提供了一个新的证明,增强了非对称边界,并使用先进的转移技术为二次分割差异函数建立了新的下界.
科学领域:
- 功能分析是一种功能分析.
- 律分析 律分析
- 运算子理论 运算子理论
背景情况:
- 双线舒尔乘法在分析函数空间和运算理论方面至关重要.
- 波塔波夫,斯克里普卡和苏科切夫以前的工作使用光谱转移函数证明了Koplienko的猜想.
- 对于二次数除差函数的双线舒尔乘法器的现有边界缺乏最佳的表征.
研究的目的:
- 为二次数除差函数的双线舒尔乘数的局限性提供一个新的证明.
- 为了显著提高这些乘数的已知非对称边界.
- 为这些二线式舒尔乘数建立一个新的,改进的下界.
主要方法:
- 利用了近期双线转移技术的进展.
- 应用了霍尔曼德-米克林-舒尔乘法定理.
- 开发了一种新的方法来推导上下边界.
主要成果:
- 建立了对二次数除差函数的双线Schur乘法器的敏的非对称边界.
- 衍生出一个新的下界,改进了之前已知的科因,勒梅迪,波塔波夫,苏科切夫和姆斯科娃的结果.
- 对于特定的参数范围,证明了推导估计D (p, 2p, 2p) 的最佳性.
结论:
- 新的证明提供了对二线式舒尔乘数的精细理解.
- 改进的边界提供了更精确的这些运营商的特征.
- 确定的最佳性突出显示了该领域新成果的重要性.
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