Exact n -width on the class of analytic functions in the space of continuous functions

摘要

Let ω(-) be a given concave modulus of continuity and ω (g, - ) be the modulus of continuity of a function g ∈ C, where C is the space of 2π-periodic, continuous functions on R with norm ||f||_c:=max|g(t)|, h~(r,ω)_(∞,β)( r — 0, 1,2,... ) denotes those 2π-periodic, real-valued functions / on R that are analytic in the strip S_β:={z ∈C:|Imz|<β}, β>0, and satisfy the restriction condition: ω(f~((r)), - )=≤ω(-) . In this paper, the exact n-width of the class of functions h~(r,ω)_(∞,β) in the space C is determined.