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Upper bounds for eigenvalues of Cauchy-Hankel tensors

Frontiers of Mathematics in China, ISSN: 1673-3576, Vol: 16, Issue: 4, Page: 1023-1041
2021
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Article Description

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 l into l (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, sufficient and necessary conditions of M-positive definiteness are obtained, and an upper bound of M-eigenvalue is also shown.

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