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Existence of Hypersingular Integrals with a Power Singularity of Arbitrary Integer Order

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Abstract

The existence of a hypersingular integral on an interval with a singularity of arbitrary integer order is considered. It is shown that the equivalence of ways of introducing a hypersingular integral in the sense of a Hadamard finite part and on the basis of a formal introduction in the integrand of the derivative with respect to the parameter of the singular Cauchy integral, understood in the sense of its principal value. Sufficient conditions are formulated for the existence of such integrals.

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REFERENCES

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, 119991, Moscow, Russia

    A. V. Setukha & S. V. Sukmanyuk

Authors
  1. A. V. Setukha
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  2. S. V. Sukmanyuk
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Correspondence to A. V. Setukha or S. V. Sukmanyuk.

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Translated by I. Tselishcheva

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Setukha, A.V., Sukmanyuk, S.V. Existence of Hypersingular Integrals with a Power Singularity of Arbitrary Integer Order. MoscowUniv.Comput.Math.Cybern. 45, 126–133 (2021). https://doi.org/10.3103/S0278641921030067

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  • DOI: https://doi.org/10.3103/S0278641921030067

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