Geodesic
Green's Functions for Singular Ordinary Differential Operators
Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 571-582

Voir la notice de l'article provenant de la source Cambridge University Press

There are several ways to approach the eigenfunction expansion problem for ordinary differential operators via the spectral theorem for self-ad joint linear operators in Hilbert space. One can examine the resolvent, which requires a detailed study of the Green's function (4, 5, 7), or one can use the spectral theorem for unbounded operators (2, 3, 9). Since the eigenf unction expansion theorem also requires some multiplicity theory, unless one is prepared to use a rather powerful form of the spectral theorem for unbounded operators, as in (2, 9), the proof requires a good deal of work in addition to the spectral theorem. 
Brauer, Fred. Green's Functions for Singular Ordinary Differential Operators. Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 571-582. doi: 10.4153/CJM-1967-050-5
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