Some Trigonometric Polynomials with Extremally Small Uniform Norm
Matematičeskie zametki, Tome 98 (2015) no. 2, pp. 196-203 Cet article a éte moissonné depuis la source Math-Net.Ru

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An example of trigonometric polynomials with extremally small uniform norm is given. This example shows the extent to which Sidon's inequality for lacunary polynomials can be generalized in a certain direction.
Keywords: trigonometric polynomial, lacunary polynomial, Sidon's inequality, Carleson–Hunt inequality.
Mots-clés : Fejér kernel
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P. G. Grigor'ev; A. O. Radomskii. Some Trigonometric Polynomials with Extremally Small Uniform Norm. Matematičeskie zametki, Tome 98 (2015) no. 2, pp. 196-203. http://geodesic.mathdoc.fr/item/MZM_2015_98_2_a4/

[1] P. G. Grigorev, “Ob odnoi posledovatelnosti trigonometricheskikh polinomov”, Matem. zametki, 61:6 (1997), 935–938 | DOI | MR | Zbl

[2] A. O. Radomskii, “O vozmozhnosti usileniya neravenstv tipa Sidona”, Matem. zametki, 94:5 (2013), 792–795 | DOI | MR | Zbl

[3] A. Zigmund, Trigonometricheskie ryady, Mir, M., 1965 | MR | Zbl | Zbl

[4] B. S. Kashin, V. N. Temlyakov, “Ob odnoi norme i svyazannykh s nei prilozheniyakh”, Matem. zametki, 64:4 (1998), 637–640 | DOI | MR | Zbl

[5] B. S. Kashin, V. N. Temlyakov, “Ob odnoi norme i approksimatsionnykh kharakteristikakh klassov funktsii mnogikh peremennykh”, Metricheskaya teoriya funktsii i smezhnye voprosy analiza, red. S. M. Nikolskii, Izd-vo AFTs, M., 1999, 69–99 | MR

[6] B. S. Kashin, V. N. Temlyakov, “Ob odnoi norme i approksimatsionnykh kharakteristikakh klassov funktsii mnogikh peremennykh”, Teoriya funktsii, SMFN, 25, RUDN, M., 2007, 58–79 | MR | Zbl

[7] A. O. Radomskii, “Ob odnom neravenstve tipa Sidona dlya trigonometricheskikh polinomov”, Matem. zametki, 89:4 (2011), 589–595 | DOI | MR | Zbl

[8] P. G. Grigorev, Sluchainye i spetsialnye polinomy po obschim funktsionalnym sistemam, Dis. $\dots$ kand. fiz.-matem. nauk, MIAH, M., 2002

[9] R. A. Hunt, “On the convergence of Fourier series”, Orthogonal Expansions and Their Continuous Analogues (Edwardsville, IL, 1967), Southern Illinois Univ. Press, Carbondale, IL, 1968, 235–255 | MR | Zbl