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

Abstract

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 denotes those 2π-periodic, real-valued functions f 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˜_∞,β ^r,ω in the space C is determined.

Keywords:

• analytic function
• concave modulus of continuity
• n-width