Geodesic
Sidon-Type Inequalities and the Space of Quasi-continuous Functions
Informatics and Automation, Approximation Theory, Functional Analysis, and Applications, Tome 319 (2022), pp. 268-279.

Voir la notice de l'article provenant de la source Math-Net.Ru

We discuss various results on Sidon-type inequalities and on the space of quasi-continuous functions.
Keywords: trigonometric polynomial, lacunary sequence, Riesz product, Rademacher functions, Walsh system
Mots-clés : Hadamard matrix. 
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Artyom O. Radomskii. Sidon-Type Inequalities and the Space of Quasi-continuous Functions. Informatics and Automation, Approximation Theory, Functional Analysis, and Applications, Tome 319 (2022), pp. 268-279. http://geodesic.mathdoc.fr/item/TRSPY_2022_319_a16/

[1] P. G. Grigor'ev, “On a sequence of trigonometric polynomials”, Math. Notes, 61:6 (1997), 780–783 | DOI

[2] P. G. Grigor'ev and A. O. Radomskii, “Some trigonometric polynomials with extremally small uniform norm”, Math. Notes, 98:1–2 (2015), 230–236 | DOI | MR

[3] M. Hall, Combinatorial Theory, Blaisdell Publ. Co., Waltham, MA, 1967 | MR

[4] B. S. Kashin and A. A. Saakyan, Orthogonal Series, Transl. Math. Monogr., 75, Am. Math. Soc., Providence, RI, 1989 | MR

[5] B. S. Kashin and V. N. Temlyakov, “On a certain norm and related applications”, Math. Notes, 64:4 (1998), 551–554 | DOI | MR

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

[7] Pisier G., “De nouvelles caractérisations des ensembles de Sidon”, Mathematical analysis and applications: Essays dedicated to Laurent Schwartz on the occasion of his 65th birthday, Part B, Adv. Math. Suppl. Stud., 7, Acad. Press, New York, 1981, 685–726 | MR

[8] Pisier G., “Conditions d'entropie et caractérisations arithmétiques des ensembles de Sidon”, Topics in modern harmonic analysis: Proc. semin. (Torino and Milano, 1982), v. II, Ist. Naz. Alta Mat. Francesco Severi, Rome, 1983, 911–944 | MR

[9] Pisier G., “Arithmetic characterizations of Sidon sets”, Bull. Amer. Math. Soc., 8:1 (1983), 87–89 | DOI | MR

[10] Rademacher H., “Einige Sätze über Reihen von allgemeinen Orthogonalfunktionen”, Math. Ann., 87 (1922), 112–138 | DOI | MR

[11] A. O. Radomskii, “On the possibility of strengthening Sidon-type inequalities”, Math. Notes, 94:5–6 (2013), 829–833 | DOI | MR

[12] A. O. Radomskii, “$\mathrm {QC}$-norm of trigonometric polynomials of special form”, Moscow Univ. Math. Bull., 70:2 (2015), 84–87 | DOI | MR

[13] A. O. Radomskii, “On nonequivalence of the $\mathrm {C}$- and $\mathrm {QC}$-norms in the space of trigonometric polynomials”, Sb. Math., 207:12 (2016), 1729–1742 | DOI | MR

[14] A. O. Radomskii, “On a Sidon-type inequality for discrete orthonormal systems”, Math. Notes, 101:3–4 (2017), 693–698 | DOI | MR

[15] A. O. Radomskii, “On the Sidon inequality for trigonometric polynomials”, St. Petersburg Math. J., 29:4 (2018), 643–656 | DOI | MR

[16] A. O. Radomskii, “Some trigonometric polynomials with extremely small uniform norm and their applications”, Izv. Math., 84:2 (2020), 361–391 | DOI | MR

[17] Riesz F., “Über die Fourierkoeffizienten einer stetigen Funktion von beschränkter Schwankung”, Math. Z., 2 (1918), 312–315 | DOI | MR

[18] Sidon S., “Verallgemeinerung eines Satzes über die absolute Konvergenz von Fourierreihen mit Lücken”, Math. Ann., 97 (1927), 675–676 | DOI | MR

[19] Sidon S., “Über orthogonale Entwicklungen”, Acta sci. math. Szeged, 10 (1943), 206–253 | MR

[20] Stechkin S.B., “Ob absolyutnoi skhodimosti ryadov Fure (trete soobschenie)”, Izv. AN SSSR. Ser. mat., 20:3 (1956), 385–412