Vazgen Mikayelyan's publications
Publication: Article
Gibbs Phenomenon for Stromberg Systems
Vol. 117 No. 3 pp. 187-191 (2017)
The Gibbs phenomenon for general Franklin systems
Vol. 52 No. 4 pp. 198–210 (2017)
On Convergence of Partial Sums of Franklin Series to +∞
Vol. 54 No. 6 pp. 347-354 (2019)
URL: https://link.springer.com/article/10.3103/S1068362319060049
DOI: https://doi.org/10.3103/S1068362319060049
Description: In this paper, we prove that if {nk} is an arbitrary increasing sequence of natural numbers such that the ratio nk+1/nk is bounded, then the nk-th partial sum of a series by Franklin system cannot converge to +∞ on a set of positive measure. Also, we prove that if the ratio nk+1/nk is unbounded, then there exists a series by Franklin system, the nk-th partial sum of which converges to +∞ almost everywhere on [0, 1].
The Gibbs Phenomenon for Stromberg’s Piecewise Linear Wavelet
Vol. 54 No. 2 pp. 112-123 (2019)
URL: https://link.springer.com/article/10.3103/S1068362319020080
DOI: https://doi.org/10.3103/S1068362319020080
Description: In this paper we study the Gibbs phenomenon for a Stromberg’s piecewise linear wavelet.We prove that the Gibbs phenomenon for partial sums of Fourier-Stromberg series occurs at all points of R and the Gibbs function is almost everywhere equal to 1+23√3 .
On a “Martingale Property” of Series with Respect to General Franklin System
Vol. 120 No. 2 pp. 110-114 (2020)
On a Property of the Franklin System in C[0, 1] and L^1[0, 1]
Vol. 107 No. 2 pp. 284-287 (2020)
The Gibbs phenomenon for Stromberg wavelets
Vol. 96 No. 3 pp. 23-27 (2020)