Geodesic
Generalization of a Mendeleeff problem
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (1988), pp. 3-10.

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In this work for the polynomials $$P_n(x)=a_0+\sum\limits^m_{k=1}x^{\gamma_k}\sum\limits_{v=1}^{\mu_k-1}a_{k,v}(\ln x)^v$$ with $$||P_n ||_{L^2(0, 1)}=M, \mu_k\in N, k=1,2,\dots,m,~ \sum\limits_{k=1}^m\mu_k=n,$$ the problem of estimation of the coefficients $a$ is solved. Also the explicit form of the extremal polynom is given. 
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G. V. Badalyan; V. M. Edigarian. Generalization of a Mendeleeff problem. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (1988), pp. 3-10. http://geodesic.mathdoc.fr/item/UZERU_1988_1_a0/

[1] A. A. Markoff, “Mémoire sur la transformation des séries peu convergentes en séries très convergentes”, Mémoires de l'Académie Impériale des Sciences de St.-Pétersbourg, 52 (1890), 1–24

[2] S. Bernstein, “Leçons sur les proprietés extremales et la meilleure approximation des fonctions analytiques d'une variable relle”, Collection Borel, Gauthier-Villar, Paris, 1926, 213 pp. | Zbl

[3] L. Schwartz, Étude des sommes d'exponentielles, Hermann, Paris, 1959 | MR | Zbl