On Faber--Schauder coefficients of continuous functions and divergence of greedy algorighms
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2019), pp. 63-69.

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We consider relationship between the rate of convergence to zero of the Faber–Schauder coefficients of continuous functions and the behavior of the greedy algorithm. We construct a continuous function f with Faber–Schauder coefficients |An(f)|=O(log1n) and divergent greedy algorithm.
Mots-clés : greedy algorithm, Faber–Schauder system, coefficients of expansion, uniform convergence.
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     title = {On {Faber--Schauder} coefficients of continuous functions and divergence of greedy algorighms},
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A. A. Sargsyan. On Faber--Schauder coefficients of continuous functions and divergence of greedy algorighms. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2019), pp. 63-69. https://geodesic-test.mathdoc.fr/item/IVM_2019_5_a5/

[1] Schauder J., “Zur Theorie stetiger Abbildungen in Functionalraumen”, Math. Zeit., 26 (1927), 47–65 | DOI | MR | Zbl

[2] Temlyakov V. N., “Nonlinear methods of approximation”, Found. Comput. Math., 3:1 (2003), 33–107 | DOI | MR | Zbl

[3] DeVore R. A., Temlyakov V. N., “Some remarks on greedy algorithms”, Adv. Comput. Math., 5:2–3 (1996), 173–187 | DOI | MR | Zbl

[4] Konyagin S. V., Temlyakov V. N., “A remark on greedy approximation in Banach spaces”, East J. Approx., 5:3 (1999), 365–379 | MR | Zbl

[5] Wojtaszczyk P., “Greedy algorithm for general biorthogonal systems”, J. Approx. Theory, 107:2 (2000), 293–314 | DOI | MR | Zbl

[6] Körner T. W., “Divergence of decreasing rearranged Fourier series”, Ann. Math., 144:1 (1996), 167–180 | DOI | MR | Zbl

[7] Grigoryan M. G., “O skhodimosti v metrike $L^p$ gridi algoritma po trigonometricheskoi sisteme”, Izv. NAN Armenii, 4 (2004), 89–116

[8] Grigoryan M. G., Gogyan S. L., “On nonlinear approximation with respect to the Haar system and modifications of functions”, Anal. Math., 32:1 (2006), 49–80 | DOI | MR | Zbl

[9] Gogyan S. L., “Greedy algorithm with regard to Haar subsystems”, East J. Approx., 11:2 (2005), 221–236 | MR | Zbl

[10] Dilworth S. J., Kalton N. J., Kutzarova D., “On the existence of almost greedy bases in Banach spaces”, Studia Math., 159:1 (2003), 67–101 | DOI | MR | Zbl

[11] Sargsyan A. A., “Svoistvo kvazigridi sistemnosti nekotorykh podsistem sistemy Fabera–Shaudera”, Izv. NAN Arm., 40:3 (2005), 46–54 | MR | Zbl

[12] Sargsyan A. A., “O kvazigridi sistemnosti i demokratichnosti nekotorykh podsistem sistemy Fabera–Shaudera”, Izv. NAN Arm., 41:2 (2006), 56–73

[13] Grigoryan M. G., Sargsyan A. A., “Nelineinaya approksimatsiya nepreryvnykh funktsii po sisteme Fabera–Shaudera”, Matem. sb., 199:5 (2008), 3–26 | DOI | MR

[14] Ulyanov P. L., “Predstavlenie funktsii ryadami i klassy $\varphi(L)$”, UMN, 27:2 (1972), 3–52 | MR | Zbl

[15] Fikhtengolts G. M., Kurs differentsialnogo i integralnogo ischisleniya, v. 2, Nauka, M., 1970