Integral representation of 2π–periodic and trigonometrically convex functions

Abstract

The integral representation given by Levin [1, p. 60, Theorem 24] of 2π-periodic and ρ-trigonometrically convex functions which are indicators of holomorphic functions of non-zero finite order ρ is incorrect. Counterexamples are given here as weii as a corrected version of the representation.

AMS No:

• 30D15