Geodesic
Recovering a~function from its trigonometric integral
Sbornik. Mathematics, Tome 201 (2010) no. 7, pp. 1053-1068

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{SM_2010_201_7_a5,
     author = {T. A. Sworowska},
     title = {Recovering a~function from its trigonometric integral},
     journal = {Sbornik. Mathematics},
     pages = {1053--1068},
     publisher = {mathdoc},
     volume = {201},
     number = {7},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2010_201_7_a5/}
}
TY  - JOUR
AU  - T. A. Sworowska
TI  - Recovering a~function from its trigonometric integral
JO  - Sbornik. Mathematics
PY  - 2010
SP  - 1053
EP  - 1068
VL  - 201
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2010_201_7_a5/
LA  - en
ID  - SM_2010_201_7_a5
ER  - 
%0 Journal Article
%A T. A. Sworowska
%T Recovering a~function from its trigonometric integral
%J Sbornik. Mathematics
%D 2010
%P 1053-1068
%V 201
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2010_201_7_a5/
%G en
%F SM_2010_201_7_a5
T. A. Sworowska. Recovering a~function from its trigonometric integral. Sbornik. Mathematics, Tome 201 (2010) no. 7, pp. 1053-1068. http://geodesic.mathdoc.fr/item/SM_2010_201_7_a5/