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This article is cited in 1 scientific paper (total in 1 paper)
Scientific Part
Mathematics
Harmonic analysis of periodic at infinity functions from Stepanov spaces
I. I. Strukova Voronezh State University, 1, Universitetskaya pl., Voronezh, Russia, 394036
Abstract:
We consider Stepanov spaces of functions defined on $\mathbb{R}$ with their values in a complex Banach space. We introduce the notions of slowly varying and periodic at infinity functions from Stepanov space. The main results of the article are concerned with harmonic analysis of periodic at infinity functions from Stepanov space. For this class of functions we introduce the notion of a generalized Fourier series; the Fourier coefficients in this case may not be constants, they are functions that are slowly varying at infinity. We prove analogs of the classical results on Ćesaro summability. Basic results are derived with the use of isometric representations theory.
Key words:
Banach space, $L^1(\mathbb{R})$-module, Stepanov space, slowly varying at infinity function, periodic at infinity function, Fourier series.
Citation:
I. I. Strukova, “Harmonic analysis of periodic at infinity functions from Stepanov spaces”, Izv. Saratov Univ. Math. Mech. Inform., 17:2 (2017), 172–182
Linking options:
https://www.mathnet.ru/eng/isu714 https://www.mathnet.ru/eng/isu/v17/i2/p172
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Abstract page: | 338 | Full-text PDF : | 139 | References: | 67 |
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