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Convolution equations on a large finite interval with symbols having power-order zeros or poles. (English. Russian original) Zbl 1380.44003

J. Math. Sci., New York 226, No. 6, 711-719 (2017); translation from Zap. Nauchn. Semin. POMI 451, 29-42 (2016).
Summary: A 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 a noninteger power order in the dual variable, which leads to long-range influence. A power-order complete asymptotic expansion is found for the kernel of the inverse operator as the length of the interval tends to infinity.

MSC:

44A35 Convolution as an integral transform
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