Geodesic
On a class of one-dimensional singular pseudodifferential operators
Sbornik. Mathematics, Tome 33 (1977) no. 1, pp. 43-61 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper is devoted to studying the method of the Sonin and Poisson transmutation operators for ordinary differential operators with variable coefficients. A new class of singular pseudodifferential operators is introduced which is closed under multiplication and which contains differential operators with singular coefficients, in particular, the Bessel operator. It is shown that after application of transmutation operators the original operator with variable coefficients (even a differential operator) is transformed into a classical pseudodifferential operator. The converse is also true: a pseuddifferential operator is transformed into a singular pseudodifferential operator. In all cases formulas are given for computing the symbols. Bibliography: 6 titles. 
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I. A. Kipriyanov; V. V. Katrakhov. On a class of one-dimensional singular pseudodifferential operators. Sbornik. Mathematics, Tome 33 (1977) no. 1, pp. 43-61. http://geodesic.mathdoc.fr/item/SM_1977_33_1_a3/

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[2] J.-L. Lions, Equations differentielles operationelles et problèmes aux limites, Springer-Verlag, Berlin, 1961 | MR | Zbl

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[4] I. A. Kipriyanov, L. N. Lyakhov, “Ob odnom klasse psevdodifferentsialnykh operatorov”, DAN SSSR, 218:2 (1974), 278–280 | Zbl

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[6] B. M. Levitan, “Razlozhenie po sobstvennym funktsiyam Besselya v ryady i integraly Fure”, Uspekhi matem. nauk, VI:2 (42) (1951), 102–103 | MR