Geodesic
On exactness of some theorems on Fourier series and transforms
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part 8, Tome 159 (1987), pp. 121-127 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider necessary and sufficient condition of differentiability of the Fourier transform in the class of functions summable with a given weight. 
@article{ZNSL_1987_159_a11,
     author = {V. P. Andreev and V. A. Solov'ev},
     title = {On exactness of some theorems on {Fourier} series and transforms},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {121--127},
     year = {1987},
     volume = {159},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_159_a11/}
}
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V. P. Andreev; V. A. Solov'ev. On exactness of some theorems on Fourier series and transforms. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part 8, Tome 159 (1987), pp. 121-127. http://geodesic.mathdoc.fr/item/ZNSL_1987_159_a11/