Abstract
Conditions implying the invertibility of the integral operator
with kernelA(x, t) having discontinuities of the first kind at the pointst=x andt=1−x are found. We give explicit inversion formulas as well as applications to the problem of finding the square roots of the operatory″(x) with arbitrary boundary conditions and the problem of expansion with respect to eigenfunctions.
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A. P. Khromov, “Equiconvergence theorems for integral operators,”Mat. Sb. [Russian Acad. Sci. Sb. Math.],114 (156), No. 6, 378–405 (1981).
A. P. Khromov and A. P. Gurevich, “Equiconvergence theorems for a class of integral operators,” in:VIII Saratov Winter School [in Russian], Abstracts of the talks, Saratov (1996), p. 117.
A. P. Khromov, “On the inversion of a class of integral operators,” in:VIII Saratov Winter School [in Russian], Abstracts of the talks, Saratov (1996), p. 118.
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Translated fromMatematicheskie Zametki, Vol. 64, No. 6, pp. 932–942, December, 1998.
This research was supported by the Russian Foundation for Basic Research under grant No. 97-01-00566.
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Khromov, A.P. Inversion of integral operators with kernels discontinuous on the diagonal. Math Notes 64, 804–813 (1998). https://doi.org/10.1007/BF02313039
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DOI: https://doi.org/10.1007/BF02313039