On uniform approximations of almost periodic functions by entire functions of finite degree

Authors

  • M. F. Timan (Днепропетр. аграр. ун-т)

Abstract

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.

Published

25.09.1995

Issue

Section

Research articles

How to Cite

Timan, M. F. “On Uniform Approximations of Almost Periodic Functions by Entire Functions of Finite Degree”. Ukrains’kyi Matematychnyi Zhurnal, vol. 47, no. 9, Sept. 1995, pp. 1274–1279, https://umj.imath.kiev.ua/index.php/umj/article/view/5528.