Upper bounds for Z$ _1 $-eigenvalues of generalized Hilbert tensors

Juan Meng; Yisheng Song

doi:10.3934/jimo.2018184

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2020, Volume 16, Issue 2: 911-918. Doi: 10.3934/jimo.2018184

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Upper bounds for Z$ _1 $-eigenvalues of generalized Hilbert tensors

Juan Meng^1, and
Yisheng Song^1, ,

School of Mathematics and Information Science, Henan Normal University, XinXiang HeNan, China

^* Corresponding author: Yisheng Song
^* Corresponding author: Yisheng Song

Received: February 28, 2018

Revised: May 31, 2018

Early access: December 2018

Published: February 2020

The first author is supported by the National Natural Science Foundation of China (Grant No.11571095, 11601134, 11701154)

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The Z$ _1 $-eigenvalue of tensors (hypermatrices) was widely used to discuss the properties of higher order Markov chains and transition probability tensors. In this paper, we extend the concept of Z$ _1 $-eigenvalue from finite-dimensional tensors to infinite-dimensional tensors, and discuss the upper bound of such eigenvalues for infinite-dimensional generalized Hilbert tensors. Furthermore, an upper bound of Z$ _1 $-eigenvalue for finite-dimensional generalized Hilbert tensor is obtained also.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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