Abstract
Generalized integrals are introduced with kernels depending on the difference of the arguments taken over a domain and a smooth contour, the boundary of this domain. These kernels arise as parametrixes of first-order elliptic systems with variable coefficients. Using such integrals (with complex density over the domain and real density over the contour), representations of vector functions that are smooth in the closed domain are described. The Fredholmity of the representation obtained in the corresponding Banach spaces is established.
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Funding
The work of M. Otelbaev was supported by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (grant no. AR 08857604).
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Translated by E. Chernokozhin
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Otelbaev, M., Soldatov, A.P. Integral Representations of Vector Functions Based on the Parametrix of First-Order Elliptic Systems. Comput. Math. and Math. Phys. 61, 964–973 (2021). https://doi.org/10.1134/S0965542521030143
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DOI: https://doi.org/10.1134/S0965542521030143