Geodesic
Convolution equations on expanding interval with symbols having zeros or poles of nonintegral power
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 46, Tome 451 (2016), pp. 29-42
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The class of convolution equations on a large expanding interval is considered. The equations are characterized by the fact that the symbol of the corresponding operator has zeros or poles of the non-integer power in the dual variable, which leads to long-range influence. The power-order complete asymptotic expantions for kernel of the inverse operator while length of the interval tends to infinity is found. 
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A. M. Budylin; S. V. Sokolov. Convolution equations on expanding interval with symbols having zeros or poles of nonintegral power. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 46, Tome 451 (2016), pp. 29-42. http://geodesic.mathdoc.fr/item/ZNSL_2016_451_a2/

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