Approximation Characteristics Of Infinite Dimensional Sequence Spaces In Different Setting

Width is one of the important contents of the function approximation theory,and is also closely related to the computational complexity.The width of some important function spaces(such as Sobolev space,Beasov function space,etc.)has been deeply studied,and a series of profound and beautiful results have been obtained.Generally speaking,the width of function space is transformed into the width of sequence space,so it is of great significance to study the width of sequence space.In this paper,the width of infinite dimensional real sequence space in worst case and probability setting is studied,and the exact asymptotic order of width of infinite dimensional sequence space is estimated by converting the width of infinite dimensional sequence space to the width of corresponding width of finite dimensional sequence space.