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Sbornik: Mathematics, 2010, Volume 201, Issue 7, Pages 1053–1068
DOI: https://doi.org/10.1070/SM2010v201n07ABEH004102 (Mi sm7588) 		 
Recovering a function from its trigonometric integral

T. A. Sworowska

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (250 kB)
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DOI: https://doi.org/10.1070/SM2010v201n07ABEH004102
Abstract: The approximate symmetric Henstock-Kurzweil integral is shown as solving the problem of the recovery of a function from its trigonometric integral. This being so, we generalize Offord's theorem, which is an analogue of de la Vallée Poussin's theorem for trigonometric series. A new condition for a function to be representable by a singular Fourier integral is also obtained.
Bibliography: 10 titles.
Keywords: trigonometric integral, approximate symmetric integral, Preiss-Thomson theorem, Offord's theorem, singular Fourier integral.
Received: 10.06.2009 and 03.12.2009
Russian version:
Matematicheskii Sbornik, 2010, Volume 201, Number 7, Pages 121–136
DOI: https://doi.org/10.4213/sm7588
Bibliographic databases:
Document Type: Article
UDC: 517.52
MSC: 26A36, 26A39
Language: English
Original paper language: Russian
Citation: T. A. Sworowska, “Recovering a function from its trigonometric integral”, Sb. Math., 201:7 (2010), 1053–1068
Citation in format AMSBIB
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\paper Recovering a~function from its trigonometric integral
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\vol 201
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  • https://www.mathnet.ru/eng/sm/v201/i7/p121
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    		Математический сборник Sbornik: Mathematics
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    Abstract page:568
    Russian version PDF:226
    English version PDF:11
    References:76
    First page:28
     
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