Recovering a function from its trigonometric integral
2010; IOP Publishing; Volume: 201; Issue: 7 Linguagem: Inglês
10.1070/sm2010v201n07abeh004102
ISSN1468-4802
AutoresTat'yana Aleksandrovna Sworowska,
Tópico(s)Mathematical functions and polynomials
ResumoThe 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 Vallee 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.
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