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Estimates for generalized derivatives of quasipolynomials from Muntz system. (English. Russian original) Zbl 1302.42040

J. Contemp. Math. Anal., Armen. Acad. Sci. 48, No. 6, 356-366 (2013); translation from Izv. Nats. Akad. Nauk Armen., Mat. 48, No. 6, 101-111 (2013).
Summary: L. Schwartz has obtained estimates for coefficients of quasipolynomials from Muntz system. In this paper we obtain exact estimates for generalized derivatives of such quasipolynomials on the interval \([0, 1]\).

MSC:

42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
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References:

[1] L. Schwartz, ”Êtuade des sommer d’exponentielles réelles”, Actualites Scientifiques et industrielles, 959, 1943.
[2] G. V. Badalyan, V. Edigaryan, ”A generalization of Mendeleev’s problem”, Abrtracts of Communications of All-Union symposium on the aproximation theory in complex domains, Ufa, June, 1987.
[3] G. V. Badalyan, ”A generalization of Legendre polynomials and their some applications”, Izv. AN Arm. SSR, ser. fizmat, estestv. and tech. nauk, 8(5), 1–28, 1955.
[4] G. V. Badalyan, ”Generalized factorial series”, Commun. of Institute ofMath. and Mech. AN Arm. SSR, 5, 13–64, 1950.
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