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# Infinite and finite dimensional generalized Hilbert tensors

Submit Time: 2017-07-03
Author: Wei Mei 河南师范大学 ; Yisheng Song 河南师范大学 ;
Institute: 1.School of Mathematics and Information Science, Henan Normal University, XinXiang HeNan, P.R. China, 453007;

## Abstracts

 In this paper, we introduce the concept of an m-order n-dimensional generalized Hilbert tensor \mathcal{H}_{n}=(\mathcal{H}_{i_{1}i_{2}\cdots i_{m}}), \mathcal{H}_{i_{1}i_{2}\cdots i_{m}}=\frac{1}{i_{1}+i_{2}+\cdots i_{m}-m+a},\ a\in \mathbb{R}\setminus\mathbb{Z}^-;\ i_{1},i_{2},\cdots,i_{m}=1,2,\cdots,n, and show that its H-spectral radius and its Z-spectral radius are smaller than or equal to M(a)n^{m-1} and M(a)n^{\frac{m}{2}}, respectively, here M(a) is a constant only dependent on a. Moreover, both infinite and finite dimensional generalized Hilbert tensors are positive definite for a\geq1. For an m-order infinite dimensional generalized Hilbert tensor \$\mathcal{H}_{\infty} with a>0, we prove that \mathcal{H}_{\infty} defines a bounded and positively (m-1)-homogeneous operator from l^{1} into l^{p}\ (1
From: 宋义生
DOI：10.1016/j.laa.2017.05.052
Recommended references： Wei Mei,Yisheng Song.(2017).Infinite and finite dimensional generalized Hilbert tensors.doi:10.1016/j.laa.2017.05.052 (Click&Copy)
Version History
[V1] 2016-11-16 19:42:57 chinaXiv:201611.00887v1(View This Version) Download
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