Upper bounds for eigenvalues of Cauchy-Hankel tensors

doi:10.1007/s11464-021-0890-0

Front. Math. China

2021, Vol. 16

Issue (4) : 1023-1041 https://doi.org/10.1007/s11464-021-0890-0

RESEARCH ARTICLE

Upper bounds for eigenvalues of Cauchy-Hankel tensors

Wei MEI¹, Qingzhi YANG^1,²(

)

¹. School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China
². School of Mathematics and Statistics, Kashi University, Kashi 844006, China

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Abstract

We present upper bounds of eigenvalues for finite and infinite dimensional Cauchy-Hankel tensors. It is proved that an m-order infinite dimensional Cauchy-Hankel tensor defines a bounded and positively (m－1)-homogeneous operator from l¹ into l^p (1<p<∞); and two upper bounds of corresponding positively homogeneous operator norms are given. Moreover, for a fourth-order real partially symmetric Cauchy-Hankel tensor, suffcient and necessary conditions of M-positive definiteness are obtained, and an upper bound of M-eigenvalue is also shown.

Keywords Cauchy-Hankel tensor eigenvalues upper bound M-positive definite

Corresponding Author(s): Qingzhi YANG

Issue Date: 11 October 2021

Cite this article:

Wei MEI,Qingzhi YANG. Upper bounds for eigenvalues of Cauchy-Hankel tensors[J]. Front. Math. China, 2021, 16(4): 1023-1041.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-021-0890-0
https://academic.hep.com.cn/fmc/EN/Y2021/V16/I4/1023

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