The cross-dimensional dynamical systems have received increasing research attention in recent years.This paper characterizes the structure features of the cross-dimensional vector space.Specifically,it is proved that ...The cross-dimensional dynamical systems have received increasing research attention in recent years.This paper characterizes the structure features of the cross-dimensional vector space.Specifically,it is proved that the completion of cross-dimensional vector space is an infinite-dimensional separable Hilbert space.Hence,it means that one can isometrically and linearly embed the crossdimensional vector space into theℓ^(2),which is known as the space of square summable sequences.This result will be helpful in the modeling and analyzing the dynamics of cross-dimensional dynamical systems.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.61673129the Key Programs in Shaanxi Province of China under Grant No.2021JZ-12Science and the Technology Bureau Project of Yulin under Grant Nos.2019-89-2 and 2019-89-4。
文摘The cross-dimensional dynamical systems have received increasing research attention in recent years.This paper characterizes the structure features of the cross-dimensional vector space.Specifically,it is proved that the completion of cross-dimensional vector space is an infinite-dimensional separable Hilbert space.Hence,it means that one can isometrically and linearly embed the crossdimensional vector space into theℓ^(2),which is known as the space of square summable sequences.This result will be helpful in the modeling and analyzing the dynamics of cross-dimensional dynamical systems.
