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Projection Method for a Class of Integral Operators with Bihomogeneous Kernels

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Abstract

We consider the multidimensional integral operators with bihomogeneous kernels in the L2-space. For such operators, the necessary and sufficient conditions for invertibility is obtained. The main result of the article is the applicability criterion of the projection method to a given class of operators with bihomogeneous kernels.

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Funding

The work was supported by the Regional Scientific and Educational Mathematical Center of the Southern Federal University, agreement of the Ministry of Education and Science of Russia no. 075-02-2022-893.

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Authors and Affiliations

  1. Institute of Mathematics, Mechanics and Computer Science, Regional Scientific and Educational Mathematical Center, Southern Federal University, 344090, Rostov-on-Don, Russia

    O. G. Avsyankin

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  1. O. G. Avsyankin
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Correspondence to O. G. Avsyankin.

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Avsyankin, O.G. Projection Method for a Class of Integral Operators with Bihomogeneous Kernels. Russ Math. 67, 1–8 (2023). https://doi.org/10.3103/S1066369X23030015

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  • DOI: https://doi.org/10.3103/S1066369X23030015

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