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Mat. Sb., 2010, Volume 201, Number 7, Pages 121–136 (Mi msb7588)  

Recovering a function from its trigonometric integral

T. A. Sworowska

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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.

DOI: https://doi.org/10.4213/sm7588

Full text: PDF file (503 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2010, 201:7, 1053–1068

Bibliographic databases:

Document Type: Article
UDC: 517.52
MSC: 26A36, 26A39
Received: 10.06.2009 and 03.12.2009

Citation: T. A. Sworowska, “Recovering a function from its trigonometric integral”, Mat. Sb., 201:7 (2010), 121–136; Sb. Math., 201:7 (2010), 1053–1068

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