
Minimax Theory and its Applications 02 (2017), No. 2, 231248 Copyright Heldermann Verlag 2017 New Classes of Positive SemiDefinite Hankel Tensors Qun Wang Dept. of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong wangqun876@gmail.com Guoyin Li Dept. of Applied Mathematics, University of New South Wales, Sydney 2052, Australia g.li@unsw.edu.au Liqun Qi Dept. of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong maqilq@polyu.edu.hk Yi Xu Dept. of Mathematics, Southeast University, Nanjing 210096, P. R. China yi.xu1983@gmail.com A Hankel tensor is called a strong Hankel tensor if the Hankel matrix generated by its generating vector is positive semidefinite. It is known that an even order strong Hankel tensor is a sumofsquares tensor, and thus a positive semidefinite tensor. The SOS decomposition of strong Hankel tensors has been wellstudied by W. Ding, L. Qi and Y. Wei [Inheritance properties and sumofsquares decomposition of Hankel tensors: theory and algorithms, BIT Numerical Mathematics (2016)]. On the other hand, very little is known for positive semidefinite Hankel tensors which are not strong Hankel tensors. In this paper, we study some classes of positive semidefinite Hankel tensors which are not strong Hankel tensors. These include truncated Hankel tensors and quasitruncated Hankel tensors. Then we show that a strong Hankel tensor generated by an absoluate integrable function is always completely decomposable, and give a class of SOS Hankel tensors which are not completely decomposable. Keywords: Hankel tensors, generating vectors, positive semidefiniteness, strong Hankel tensors. MSC: 15A18, 15A69. [ Fulltextpdf (133 KB)] for subscribers only. 