Email this article The Gibbs phenomenon for general Franklin systems
- Authors: Mikayelyan V.G.1
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Affiliations:
- Yerevan State University
- Issue: Vol 52, No 4 (2017)
- Pages: 198-210
- Section: Real and Complex Analysis
- URL: https://journal-vniispk.ru/1068-3623/article/view/228067
- DOI: https://doi.org/10.3103/S1068362317040069
- ID: 228067
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Abstract
The paper is devoted to the Gibbs phenomenon for series by general Franklin systems. The general Franklin system corresponding to a given dense sequence of points T = (tn, n ≥ 0) in [0, 1] is a sequence of orthonormal piecewise linear functions with knots from T, that is, the nth function from the system has knots t0,..., tn. The main result of this paper is that the Gibbs phenomenon for Fourier series by general Franklin systems occurs for almost all points of [0, 1].
About the authors
V. G. Mikayelyan
Yerevan State University
Author for correspondence.
Email: mik.vazgen@gmail.com
Armenia, Yerevan
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