Harmonic Analysis of Functions Periodic at Infinity


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Authors

  • Anatoly Grigor’evich Baskakov
  • Irina Igorevna Strukova

Keywords:

Banach space, functions slowly varying at infinity, functions periodic at infinity, Wiener’s theorem, absolutely convergent Fourier series, invertibility, difference equations

Abstract

In this paper we introduce the notion of vector-valued functions periodic at infinity. We characterize the sums of the usual periodic functions and functions vanishing at infinity as a subclass of these functions. Our main focus is the development of the basic harmonic analysis for functions periodic at infinity and an analogue of the celebrated Wiener's Lemma that deals with absolutely convergent Fourier series. We also derive criteria of periodicity at infinity for solutions of difference and differential equations. Some of the results are derived by means of the spectral theory of isometric group representations.

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Published

2016-12-30

How to Cite

Baskakov, A. G., & Strukova, I. I. (2016). Harmonic Analysis of Functions Periodic at Infinity. Eurasian Mathematical Journal, 7(4), 09–29. Retrieved from https://emj.enu.kz/index.php/main/article/view/646

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