Geodesic
On the Structure of the Class
Matematičeskie zametki, Tome 80 (2006) no. 2, pp. 296-308

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In this paper, we study whether the set $A(\varphi)$ is closed under multiplication $f\cdot g$, where $f$ and $g$ belong to the class $A(\varphi)$. We also study the problem of the existence of a solution of the equation $Bx=\nobreak C$ (where $B,C\in A(\varphi)$ and $B\neq \nobreak 0$) on the set $A(\varphi)$.
Keywords: the class $A(\varphi)$, Banach space, Khinchine's inequality, Rademacher function, Haar system, Walsh system
Mots-clés : Fourier coefficients. 
V. Sh. Tsagareishvili. On the Structure of the Class. Matematičeskie zametki, Tome 80 (2006) no. 2, pp. 296-308. http://geodesic.mathdoc.fr/item/MZM_2006_80_2_a14/
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[1] Zh. P. Kakhan, Absolyutno skhodyaschiesya ryady Fure, Mir, M., 1976

[2] P. L. Ulyanov, “Ob absolyutnoi skhodimosti trigonometricheskikh ryadov Fure”, Dokl. AN SSSR, 322:2 (1992), 253–258 | MR | Zbl

[3] V. Bugadze, Ryady Fure–Khaara superpozitsii funktsii, Tbilisi, 1988 | MR | Zbl

[4] S. V. Bochkarev, “Absolyutnaya skhodimost ryadov Fure otnositelno obschikh ortogonalnykh polnykh sistem”, UMN, 27:1 (1972), 53–76 | MR | Zbl

[5] V. Tsagareishvili, Klassy funktsii i koeffitsienty Fure, Doktorskaya dissertatsiya, Tbilisi, 2004

[6] P. L. Ulyanov, “O ryadakh po sisteme Khaara”, Matem. sb., 63(105):3 (1964), 356–391 | MR | Zbl