Geodesic
On approximation of integral operators, their kernels, and solutions of Fredholm integral equations of the second kind in connection with an operator of Sturm-Liouville type
Izvestiya. Mathematics , Tome 42 (1994) no. 1, pp. 173-182.

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Best possible estimates of the degree of approximation are found for integral operators by finite-dimensional operators, for kernels of integral operators by bilinear expressions, and for solutions of Fredholm integral equations of the second kind by solutions of finite-dimensional problems. The class of integral operators includes the trace-class resolvent of a Sturm–Liouville operator on the whole line. 
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K. T. Mynbaev. On approximation of integral operators, their kernels, and solutions of Fredholm integral equations of the second kind in connection with an operator of Sturm-Liouville type. Izvestiya. Mathematics , Tome 42 (1994) no. 1, pp. 173-182. http://geodesic.mathdoc.fr/item/IM2_1994_42_1_a9/

[1] Besov O. V., Ilin V. P., Nikolskii S. M., Integralnye predstavleniya funktsii i teoremy vlozheniya, Nauka, M., 1975 | MR | Zbl

[2] Birman M. Sh., Solomyak M. Z., “Otsenki singulyarnykh chisel integralnykh operatorov”, UMN, 32:1 (1977), 17–84 | MR | Zbl

[3] Temlyakov V. N., “Bilineinaya approksimatsiya i prilozheniya”, Tr. MIAN SSSR, 187, 1989, 191–215 | MR

[4] Otelbaev M., “Teoremy vlozheniya prostranstv s vesom i ikh primeneniya k izucheniyu spektra operatora Shredingera”, Tr. MIAN SSSR, 150, 1979, 265–305 | MR | Zbl

[5] Gusman M., Differentsirovanie integralov v $\mathbf{R}^n$, Mir, M., 1978 | MR

[6] Schmidt E., “Zur Theorie der linearen und iiichtlinearen Integralgleihungen, 1”, Math. Ann., 63 (1907), 433–470 | DOI | MR

[7] Stechkin S. B., “O nailuchshem priblizhenii zadannykh klassov funktsii lyubymi polinomami”, UMN, 9:1 (1954), 133–134 | Zbl

[8] Ismagilov R. S., “Poperechniki mnozhestv v lineinykh normirovannykh prostranstvakh i priblizhenie funktsii trigonometricheskimi mnogochlenami”, UMN, 29:3 (1974), 161–178 | MR | Zbl

[9] Mynbaev K. T., Otelbaev M. O., Vesovye funktsionalnye prostranstva i spektr differentsialnykh operatorov, Nauka, M., 1988 | MR | Zbl

[10] Pereverzev S. V., “O slozhnosti zadachi nakhozhdeniya reshenii uravneniya Fredgolma II roda s gladkimi yadrami, II”, Ukr. matem. zhurn., 41:2 (1989), 189–193 | MR

[11] Smithies F., Proc. London Math. Soc., 43 (1937), 255–279 | DOI | Zbl