On uniform approximations of almost periodic functions by entire functions of finite degree - Timan, M. F. (Ukrains’kyi Matematychnyi Zhurnal, 1995)
We give a new proof of the well-known Bernshtein statement that, among entire functions of degree ≤ σ which realize the best uniform approximation (of degree σ) of a periodic function on (−∞,∞), there is a trigonometric polynomial of degree ≤ σ. We prove an analog of the mentioned Bernshtein statement and the Jackson theorem for uniform almost periodic functions with arbitrary spectrum.