Frontiers of Mathematics in China >
Upper bounds for eigenvalues of Cauchy-Hankel tensors
Received date: 09 Oct 2020
Accepted date: 04 Dec 2020
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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 lp (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.
Key words： Cauchy-Hankel tensor; eigenvalues; upper bound; M-positive definite
Wei MEI , Qingzhi YANG . Upper bounds for eigenvalues of Cauchy-Hankel tensors[J]. Frontiers of Mathematics in China, 2021 , 16(4) : 1023 -1041 . DOI: 10.1007/s11464-021-0890-0
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