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On the solution of integral equations by the method of integral transform. (English. Russian original) Zbl 0198.44801

Sib. Math. J. 10(1969), 1034-1042 (1970); translation from Sib. Mat. Zhurn. 10, 1395-1405 (1969).

MSC:

45A05 Linear integral equations
44A35 Convolution as an integral transform
44A10 Laplace transform
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type

Citations:

Zbl 0197.09001
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Full Text: DOI

References:

[1] E. Titchmarsh, Introduction to the Theory of the Fourier Integral [Russian translation], IL, Moscow (1948). · Zbl 0031.03202
[2] I. Sneddon, Fourier Transforms [Russian translation], IL, Moscow (1955).
[3] V. A. Ditkin and A. P. Prudnikov, Integral Transforms and Operational Calculus [in Russian], Fizmatgiz, Moscow (1961). · Zbl 0133.06202
[4] A. N. Tikhonov, ?On the solution of some ill-posed problems and a method of regularization,? Dokl. Akad. Nauk SSSR,151, No. 3, 501-504 (1963).
[5] A. N. Tikhonov, ?On the regularization of ill-posed problems? Dokl. Akad. Nauk SSSR, No. 1, 49-52 (1963).
[6] V. K. Ivanov, ?On uniform rogularization of unstable problems? Sibirsk. Matem. Zh.,7, No. 3, 546-558 (1966).
[7] M. M. Lavrent’ev and V. G. Vasil’ev, ?On the formulation of some ill-posed problems of mathematical physics,? Sibirsk. Matem. Zh.,7, No. 3, 559-576 (1966).
[8] N. N. Lebedev, Special Functions and Some of Their Applications [in Russian], Gostoptekhizdat, Moscow (1954).
[9] V. A. Fok, ?On the representation of an arbitrary function by an integral involving Legendre’s functions with a complex index,? Dokl. Akad. Nauk SSSR,39, 379-383 (1943).
[10] I. M. Ryzhik and I. S. Gradshtein, Tables of Integrals, Sums, Series and Products [in Russian], 2nd Edition, Fizmatgiz, Moscow (1962).
[11] M. M. Lavrent’ev, ?On some ill-posed problems of mathematical physics,? Izd-vo SO Akad. Nauk SSSR, Novosibirsk (1962).
[12] A. B. Bakushinskii, ?On a numerical, method for the solution of Fredholm integral equations of the 1st kind,? Sb. ?Vychislitel’nye metody i programmirovanie,? Izd.-vo MGU, No. 5 (1966).
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