Geodesic
The Two-Sided Factorization of Ordinary Differential Operators
Canadian journal of mathematics, Tome 32 (1980) no. 5, pp. 1045-1057

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

Throughout this paper we shall use I to denote a given interval, not necessarily bounded, of real numbers and C n to denote the real valued n times continuously differentiable functions on I and C 0 will be abbreviated to C. By a differential operator of order n we shall mean a linear function L:Cn → C of the form 1.1 where pn(x) ≠ 0 for x ∊ I and p i ∊ C j 0 ≦ j ≦ n. The function p n is called the leading coefficient of L.It is well known (see, for example, [2, pp. 73-74]) thai a differential operator L of order n uniquely determines both a differential operator L* of order n (the adjoint of L) and a bilinear form [·,·]L (the Lagrange bracket) so that if D denotes differentiation, we have for u, v ∊ Cn, 1.2 
Browne, Patrick J.; Nillsen, Rodney. The Two-Sided Factorization of Ordinary Differential Operators. Canadian journal of mathematics, Tome 32 (1980) no. 5, pp. 1045-1057. doi: 10.4153/CJM-1980-080-5
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