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On the new approach to the constructions of the index transforms

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  • Department of Mathematics and Mechanics, Belarussian State University, P. O. Box 385, Republic of Belarus 220050, Minsk-50
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Bibliografia
[1] A. Erdélyi et al., Higher Transcendental Functions, Vols. 1, 2, McGraw-Hill, New York, 1953.
[2] V. A. Fock, On the representation of an arbitrary function by an integral involving Legendre's functions with a complex index, Dokl. Akad. Nauk SSSR 39 (1943), 253-256.
[3] N. N. Lebedev, Sur une formule d'inversion, ibid. 52 (1946), 655-658.
[4] N. N. Lebedev, On the representation of an arbitrary function by an integral with respect to the squares of Macdonald functions of imaginary index, Sibirsk. Math. Zh. 3 (2) (1962), 213-222 (in Russian).
[5] N. N. Lebedev, Analogue of the Parseval theorem for some integral transform, Dokl. Akad. Nauk. SSSR 68 (1949), 653-656 (in Russian).
[6] N. N. Lebedev, The Parseval theorem for the Mehler-Fock integral transform, ibid., 445-448 (in Russian).
[7] N. N. Lebedev and I. P. Skalskaya, Some integral transforms related to the Kontorovich-Lebedev transform, in: Problems of Mathematics and Physics, Leningrad, 1976, 68-79 (in Russian).
[8] O. I. Marichev, Handbook of Integral Transforms of Higher Transcendental Functions, Theory and Algorithmic Tables, Ellis Horwood, Chichester, Wiley, New York, 1983.
[9] F. G. Mehler, Ueber eine mit den Kugel und Cylinderfunctionen verwandte Function und ihre Anwendung in der Theorie Elektricitats Vertheilung, Math. Ann. 18 (1881), 161-194.
[10] M. N. Olevskiĭ, On the representation of an arbitrary function by an integral with a hypergeometric function as kernel, Dokl. Akad. Nauk. SSSR 69 (1949), 11-14 (in Russian).
[11] A. P. Prudnikov et al., Integrals and Series, Gordon and Breach, New York, Vols. 1, 2, 1986, Vol. 3, 1989.
[12] Yu. M. Rappoport, Integral equations and Parseval equalities for modified Kontorovich-Lebedev integral transforms, Differentsial'nye Uravneniya 17 (1981), 1697-1699 (in Russian).
[13] E. G. Titchmarsh, Introduction to the Theory of Fourier Integrals, Oxford University Press, London and New York, 1937.
[14] Vu Kim Tuan, O. I. Marichev and S. B. Yakubovich, Composition structure of integral transformations, Soviet Math. Dokl. 33 (1986), 166-170.
[15] G. N. Watson, General transforms, Proc. London Math. Soc. 35 (1933), 156-199.
[16] J. Wimp, A class of integral transforms, Proc. Edinburgh Math. Soc. 14 (1964), 33-40.
[17] S. B. Yakubovich, Note on the inversion formula for the Wimp index integral transform, Differentsial'nye Uravneniya 21 (1985), 1097-1098 (in Russian).
[18] S. B. Yakubovich, The general integral transforms of Kontorovich-Lebedev type and their applications, Ph.D. dissertation, Minsk, 1987 (in Russian).
[19] S. B. Yakubovich, The general approach to the theory of index integral transforms, Izv. Vyssh. Uchebn. Zaved. Mat. 1986 (6), 77-79 (in Russian).
[20] S. B. Yakubovich, Vu Kim Tuan, I. O. Marichev and S. L. Kalla, A class of index integral transforms, Rev. Tec. Ing. Univ. Zulia, Edicion Especial, 10 (1) (1987), 105-118.
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