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| 2. |
- Aleksanyan, Hayk, 1987-
(författare)
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Nonlinear approximation by renormalized trigonometric system
- 2012
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Ingår i: Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences). - : Springer. - 1068-3623. ; 47:2, s. 86-96
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Tidskriftsartikel (refereegranskat)abstract
- We study the convergence of greedy algorithmwith regard to renormalized trigonometric system. Necessary and sufficient conditions are found for system’s normalization to guarantee almost everywhere convergence, and convergence in Lp(T) for 1 < p < ∞ of the greedy algorithm, where T is the unit torus. Also the non existence is proved for normalization which guarantees convergence almost everywhere for functions from L1(T), or uniform convergence for continuous functions.
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| 3. |
- Aleksanyan, Hayk, 1987-
(författare)
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On greedy algorithm by renormed Franklin system
- 2010
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Ingår i: East Journal on Approximations. - 1310-6236. ; 16:3, s. 273-296
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Tidskriftsartikel (refereegranskat)abstract
- We characterize the all weighted greedy algorithms with respect to Franklin system which converge uniformly for continuous functions and almost everywhere for integrable functions. In case, when the algorithm fails to satisfy our classification criteria, we construct a continuous function for which the corresponding approximation diverges unboundedly almost everywhere. Some applications to wavelet systems are also discussed.
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| 4. |
- Aleksanyan, Hayk, 1987-
(författare)
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On the greedy algorithm by the Haar system
- 2010
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Ingår i: Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences). - : Springer. - 1068-3623. ; 45:3, s. 151-161
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Tidskriftsartikel (refereegranskat)abstract
- The paper investigates the uniform and almost everywhere convergence of the greedy algorithm by the Haar system. Necessary and sufficient conditions for norming the functions of Haar system are obtained, which guarantee the uniformconvergence for functions from C[0, 1] and almost everywhere convergence for functions from L1[0, 1].
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| 5. |
- Aleksanyan, Hayk, 1987-
(författare)
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Regularity of boundary data in periodic homogenization of elliptic systems in layered media
- 2017
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Ingår i: Manuscripta mathematica. - : Springer-Verlag New York. - 0025-2611 .- 1432-1785. ; 154:1-2, s. 225-256
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Tidskriftsartikel (refereegranskat)abstract
- In this note we study periodic homogenization of Dirichlet problem for divergence type elliptic systems when both the coefficients and the boundary data are oscillating. One of the key difficulties here is the determination of the fixed boundary data corresponding to the limiting (homogenized) problem. This issue has been addressed in recent papers by Gérard-Varet and Masmoudi (Acta Math. 209:133–178, 2012), and by Prange (SIAM J. Math. Anal. 45(1):345–387, 2012), however, not much is known about the regularity of this fixed data. The main objective of this note is to initiate a study of this problem, and to prove several regularity results in this connection.
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