Almost periodic at infinity functions with respect to subspaces of vanishing at infinity functions

Author(s):  I. I. Strukova, candidate of Sciences, Voronezh State University, Voronezh, Russia, irina.k.post@yandex.ru

Issue:  Volume 50, № 4

Rubric:  Mathematics

Annotation:  The article under consideration is devoted to some problems of harmonic analysis of almost periodic at infinity functions. We consider different subspaces of functions vanishing at infinity and introduce the notions of slowly varying and almost periodic at infinity functions with respect to those subspaces. For periodic at infinity functions of this type we formulate four definitions and prove them to be equivalent. We also introduce the concept of a Fourier series with coefficients slowly varying at infinity (with respect to the chosen subspace) and study their properties. We prove the summability of Fourier series by the method of Bochner-Fejer. The results were received with essential use of isometric representations and Banach modules theories

Keywords:  almost periodic at infinity function, Banach space, Fourier series, Bochner-Fejer summability, Beurling spectrum, Banach module

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