Geodesic
Some trigonometric polynomials with extremely small uniform norm and their applications
Izvestiya. Mathematics , Tome 84 (2020) no. 2, pp. 361-391

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We construct orthogonal trigonometric polynomials satisfying a new spectral condition and such that their $L^{1}$-norms are bounded below and the uniform norm of their partial sums has extremely small order of growth. We obtain new results that relate the uniform norm and $\mathrm{QC}$-norm on subspaces of the vector space of trigonometric polynomials.
Keywords: trigonometric polynomial, Rademacher system.
Mots-clés : Fejér kernel 
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     author = {A. O. Radomskii},
     title = {Some trigonometric polynomials with extremely small uniform norm and their applications},
     journal = {Izvestiya. Mathematics },
     pages = {361--391},
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     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2020_84_2_a6/}
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A. O. Radomskii. Some trigonometric polynomials with extremely small uniform norm and their applications. Izvestiya. Mathematics , Tome 84 (2020) no. 2, pp. 361-391. http://geodesic.mathdoc.fr/item/IM2_2020_84_2_a6/