Geodesic
The equation of convolution on a large finite interval with the symbol which has zeros of nonintegral powers
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 45, Tome 438 (2015), pp. 83-94 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study one equation of convolution on a large finite interval. This equation arose in acoustics for a description of a wave conductor surface with a bed of ice. The main feature of this equation is that the symbol of the corresponding operator has zeros of nonintegral degrees on the dual variable so that the inverse operator is a long-range one. We found power-order complete asymptotic expansion for a kernel of the inverse operator as a length of the interval tends to infinity. 
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A. M. Budylin; S. B. Levin. The equation of convolution on a large finite interval with the symbol which has zeros of nonintegral powers. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 45, Tome 438 (2015), pp. 83-94. http://geodesic.mathdoc.fr/item/ZNSL_2015_438_a5/

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