We present upper bounds of eigenvalues for finite and infinite dimensional Cauchy-Hankel tensors.It is proved that an m-order infinite dimensional Canchy-Hankel tensor defines a bounded and positively(m-1)-homogeneous...We present upper bounds of eigenvalues for finite and infinite dimensional Cauchy-Hankel tensors.It is proved that an m-order infinite dimensional Canchy-Hankel tensor defines a bounded and positively(m-1)-homogeneous operator from l^(1)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,sufficient and necessary conditions of M-positive definiteness are obtained,and an upper bound of M-eigenvalue is also shown.展开更多
基金the National Natural Science Foundation of China(Grant Nos.11671217,12071234)the Tianjin Graduate Research and Innovation Project(No.2019YJSB040).
文摘We present upper bounds of eigenvalues for finite and infinite dimensional Cauchy-Hankel tensors.It is proved that an m-order infinite dimensional Canchy-Hankel tensor defines a bounded and positively(m-1)-homogeneous operator from l^(1)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,sufficient and necessary conditions of M-positive definiteness are obtained,and an upper bound of M-eigenvalue is also shown.
