论文标题
在Hilbert Space的多个操作员
On the Hardy-Littlewood-Pólya and Taikov type inequalities for multiple operators in Hilbert spaces
论文作者
论文摘要
我们提出了统一的方法，以获取刻薄的均匀和乘法性不平等现象，用于在希尔伯特空间上作用的多个封闭的操作员，对Hardy-Little-Polyá和Taikov类型的类型进行统一的不平等。我们将结果应用于针对紧凑型Riemmanian歧管的Laplace-Beltrami操作员的力量规范，并得出众所周知的Taikov和Hardy-Littlewood-Polyá的不平等现象，用于在$ D $ d $中的限制案例中定义的功能。其他应用程序包括线性界限对无界运算符的最佳近似值，以及按其他类别的元素对一个类的最佳近似。此外，我们为无界封闭范围的无限闭合操作员建立了尖锐的Solyar型不等式。
We present unified approach to obtain sharp mean-squared and multiplicative inequalities of Hardy-Littlewood-Polyá and Taikov types for multiple closed operators acting on Hilbert space. We apply our results to establish new sharp inequalities for the norms of powers of the Laplace-Beltrami operators on compact Riemmanian manifolds and derive the well-known Taikov and Hardy-Littlewood-Polyá inequalities for functions defined on $d$-dimensional space in the limit case. Other applications include the best approximation of unbounded operators by linear bounded ones and the best approximation of one class by elements of other class. In addition, we establish sharp Solyar-type inequalities for unbounded closed operators with closed range.
