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Izvestiya: Mathematics, 2020, Volume 84, Issue 2, Pages 361–391
DOI: https://doi.org/10.1070/IM8887 (Mi im8887) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Some trigonometric polynomials with extremely small uniform norm and their applications

A. O. Radomskii

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
English version PDF (569 kB) Citations (4)
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DOI: https://doi.org/10.1070/IM8887
Abstract: 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, Fejér kernel, Rademacher system.
Received: 01.12.2018
Revised: 27.03.2019
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2020, Volume 84, Issue 2, Pages 166–196
DOI: https://doi.org/10.4213/im8887
Bibliographic databases:
Document Type: Article
UDC: 517.5
MSC: 42A05, 46E35
Language: English
Original paper language: Russian
Citation: A. O. Radomskii, “Some trigonometric polynomials with extremely small uniform norm and their applications”, Izv. RAN. Ser. Mat., 84:2 (2020), 166–196; Izv. Math., 84:2 (2020), 361–391
Citation in format AMSBIB
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  • https://doi.org/10.1070/IM8887
  • https://www.mathnet.ru/eng/im/v84/i2/p166
    Erratum
    This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:502
    Russian version PDF:61
    English version PDF:40
    References:63
    First page:41
     
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