Geodesic
Convolution equations in a~halfspace
Sbornik. Mathematics, Tome 11 (1970) no. 3, pp. 441-457

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In this paper a necessary and sufficient condition is found for a function $\widetilde A(\xi)$ to have a factorization such that both factors are bounded from above and from below by power functions; an easily verifiable sufficient condition is also given. Further, the limits of validity of the Wiener–Hopf method are shown for equations in a halfspace with kernel depending on the difference of the arguments. Bibliography: 14 titles. 
@article{SM_1970_11_3_a9,
     author = {A. I. Shnirel'man},
     title = {Convolution equations in a~halfspace},
     journal = {Sbornik. Mathematics},
     pages = {441--457},
     publisher = {mathdoc},
     volume = {11},
     number = {3},
     year = {1970},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1970_11_3_a9/}
}
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A. I. Shnirel'man. Convolution equations in a~halfspace. Sbornik. Mathematics, Tome 11 (1970) no. 3, pp. 441-457. http://geodesic.mathdoc.fr/item/SM_1970_11_3_a9/